My idea for this timeline is based on 1) reading that one of the Polish war goals at Versailles included an independent Königsberg/East Prussia and 2) the idea that a revolting East Prussia would be the ideal place for various more and/or less crazy reactionaries to try to implent their ideas for a short time, until their government fails since one of their much more powerful opponents finished a war with another opponent. More gains to Poland could encourage East Prussian politicians to implement the "Oststaat-plan" in direct rebellion towards the German Government.
If the former is what you were aiming for, a stronger Poland that is indeed able to reduce East Prussia to a vassal-state, then that would explain the follow-thru.
If your goverment has the primary goal to remain free from Polish and Entente influence, but is also highly reactionary and could serve as a core of a counterrevolution, marching into the West would create unpredictable consequences including a highly likely civil war in Germany. Just taking the Corridor wouldn't improve the situation that much, since the German Goverment would now be forced to put far more effort in isolating East Prussia from supplies and volunteers, since a stronger East Prussia could try to be more direct in the goal of restoring the Monarchy.
The problem is that the German government in this case can't really do much to oppose the Freikorps, especially if the Reichswehr are involved as any "blockade" would be chock full of holes through which supplies and manpower could get through. The French and British would be annoyed, but they aren't willing to deploy the necessary manpower to truly cut off East Prussia from Germany by land. I'm also fairly certain that Berlin would, all and all, be glad that the Freikorps and their many sympathizers in Germany will have left for the East, as it allows some for semblance of stabilization in Germany proper (temporarily) while also collecting the most dangerous formations of the Right in one location (versus spread across the whole of Germany); they'd have time aplenty now, whilst the Freikorps are fighting the Soviets, Poles amongst others, to prepare for that eventuality where the Freikorps might turn their guns towards Berlin.
I guess large parts of the East Prussian forces are from the Freikorps and Militias fighting in the Baltics, which have in their mind the interest of gaining control over the Baltics. Is Ludendorff in my timeline powerful enough to force them to go West? I guess he has to negotiate with various commanders and leaders who think that they should have a say in all these plans.
It may have gone worse with the Prussian situation thrown into the mix, as a sizable number of the Freikorps that made their way to Latvia would have instead gone to Prussia to fight the Poles, under similar pretenses of land grants and "drag nach osten", to reclaim rightfully Germany territory. Weakened in Latvia, the Latvians and Estonians may have overrun the Germans earlier, though I'm not sure how much of a difference it would have really made. They may not have had the confidence to take down the first Latvian government, or they may have lost the race to Riga to the Estonians ... ultimately I would see the Germans as being in a worse position in the region, with what number of Freikorps that had gone there being evicted in short order once Latvia is deemed reasonably secure by the British and Latvians.
Luddendorff does not necessarily need to order them to do so; as I mentioned above, the very same reasons why the Freikorps went to Latvia would apply to any conflict between Prussia and Poland, and moreso it would additionally revolve around an idea of redeeming lands unjustly lost, they would operate from ethnically friendly areas, and logistics and finance would be less of an issue (though still an issue). There is just less risk involved for a similar reward.
Is it in the interest of the Entente to immediately blockade any ships towards East Prussia, if East Prussia could stop further Soviet influence in the Baltic until Poland is strong enough to defeat East Prussia? I doubt that Poland alone is able to supress supply by water and land at that moment.
The British at the very least were already operating in the Baltic, and the moment hostilities are opened between Poland and Prussia there is going to be serious concern over whether the Polish Republic would be able to withstand offensive actions by both them and the Soviets; any movement on the part of the Prussians to forcibly integrate the Baltic States would also be viewed unfavorably and an expansion of German power (after all, many would view Prussia simply as an appendage of the recently defeated German Empire). Basically, for quite some time Prussian influence would be seen as just as bad as Soviet influence, especially if they act as characterized.
Now again, besides a blockade I think the extent of it would be an occupation by the British (and then later the French) of both Memelland and Danzig, as those areas were designated to become mandate territories under the League of Nations anyhow, and it would reduce the number of potential ports smugglers could make use of. In the case of Memelland it would deter further Prussian expansion North, and in the case of Danzig it would complicate logistics between Prussia and Germany (at least somewhat); the combination of both could in turn then be used as a bargaining chip in any negotiations between Prussia and the Entente/Poland.
I probably need to do more research about the Memelland. But in my timeline East Prussia is already independent at the end of 1919 and claims control over the Memelland (of course in clear violation to ttl and otl Versailles), since their entire existence as an independent entity is in ttl already a clear violation of ttl Versailles. Probably I need to do more research how to prevent such a French intervention like in OTL. Of course if a french control over the Memelland would occur TTL would look entirely different.
As I've said above, I believe that a Prussian declaration of independence would necessitate a swifter approach on the part of the Entente, and so the British who were readily active in the Baltic would probably seek to occupy Memelland and Danzig in short order. Prussia would not be in any position to protest, as even the reactionaries would be hesitant to provoke either the British or French into openly joining any conflict, but barring such an event, I can't see any significant intervention on the part of France of Britain with deployments already having been made in the Middle East and Russia, and the French occupying the Ruhr.
I lack knowledge about early Soviets plans about the baltics, but it is certainly clear that their idea is different than the ideas of the Germans. In TTL there isn't peace between them, and various smaller fights between Soviets and Prussians occur in Northern Latvia. But the East Prussians in TTL decide to occupy Lithuania instead of attacking the Soviets, while the Soviets focus more on Poland.
Your arguments for a Lithuanian alliance with the Soviets are plausible in TTL at the point when East Prussian troops invade Lithuania. How would Lithuanian forces complicate the Polish-Soviet war?
Well historically it was a combination of Germans, Lithuanians and Poles that held the Soviets back. The problem here is that the Lithuanians trusted neither given that Germans had already tried to incorporate them and the Poles were trying to resurrect the Polish-Lithuanian Commonwealth as a Federal Union (or to subjugate Lithuania to Polish domination as Lithuania saw it). There came a time where the Soviets, turning their attention upon the Poles, were willing to recognize all of Lithuania's territorial claims in return for the signing of a military alliance against Poland; Lithuania hesitated only because it feared that doing so would jeopardize its chances at being recognized as an independent State in Paris by the Entente. Instead though they agreed to peace and gave the Soviets unlimited military access through Lithuanian territory, which more or less destroyed relations between Kaunus and Warsaw.
Now in the case as you've presented, you've made the German forces in Lithuania enemies of Lithuania, which means they are pressed on just about every one of their borders, and they'd be largely dependent on the Polish who aren't liable to have their support come cheap, territorial concessions being the least of Lithuania's concerns. Were the Soviet's to make the same offer, with the military situation so dire and the Entente not jumping in to rescue them anytime soon, and on top of the Poles attempting to coup the Lithuanian government, I can't see why they wouldn't take it given the alternatives. The Lithuanian military only was around (20,000) men or so at the time, which while not especially large in and of itself, would still make an impact.
Are the leading reactionaries in East Prussia and the leading nationalists in Poland ready to accept some formal ceasefire and cooperation? I guess accepting East Prussia as someone to negotiate with would in TTL weaken Polish claims of control over Danzig and Königsberg.
Neither side would be happy about it for sure, but the Polish will be struggling against the Soviets in the East following the collapse of the Kiev Offensive, and the Prussians will well be on the retreat once the Lithuanians are backed up by the Red Army; needing every man they can muster to deal with the Bolshevik threat, they simply cannot afford to have divisions deployed against one another with their other lines collapsing. It would ironically very much be like the alliance that existed between the Germans and Latvians or Germans and Lithuanians when those countries where fighting off the Soviets, one of necessity. There would be a full expectation of a return to fighting once the Soviets were dealt with.
I don't know enough about military strategy, supply and flanking to comment and/or evaluate the necessity of the Soviets to attack Königsberg and Danzig to win against Poland.
It doesn't make a lot of strategic sense to push deep into Poland exclusively, leaving the Prussians with the ability to punch behind your main line of attack; to do so would risk encircling your main armies at the front, or potentially complicate supply lines as the front line gets increasingly warped. To move against East Prussia in conjunction with Central Poland removes that risk, or at least seriously lessens it.
That sounds like a plausible scenario, if you manage to get sucsessful negotiations between East Prussia and Poland.
They could certainly come to blows again, but I figured that the willpower to keep fighting would be gone by that point, much as the two nations might hate one another.