Yeah-nah. The East Prussion territory along the Russian advance(s) was not considered particularly valuable. German military doctrine ordinarily prioritised decisive battle (i.e. destroying enemy armies) ahead of territorial considerations, for example the OTL wargame resembling the actual Battle of Tattenburg. Further, I am not certain German rail infrastructure in East Prussia could have deployed two German armies any faster than it deployed one.
Why? The Russian armies on paper would still have a modest superiority in numbers, which the Russian leadership believed would being them victory. The Russian Armies are more likely to be engaged concurrently, or at least the second (1st) Russian Army engaged before the fate of the first (2nd) Russian Army is sealed. Something identical to the Battle of Tannenberg is not inevitable, but I think it is reassonable to assume the cumalative fate of the Russian 1st and 2nd armies is likely to be worse than OTL - to the extent those armies cease to be a consideration for the balance of 1914 (at a minimum).
Why would the Russians be any better at recognising a trap in this scenario. Prima facie, the Russian 1st Army would also be hit before any trap was fully recognised.
The unspectacular grind in the west will likely cost hundreds of thousands of German lives, but far more French lives. I also think the early Russian losses, coupled with an inabilty of the French to make significant impact on German defenses is likely to result in an early finish - before any major combatant is truely exhausted - obviously Serbia is screwed.
A lot depends upon the scale and speed of deploying German troops. My understanding is that rail capacity can get two "smaller" Armies (6 to 10 Divisions plus a Cavalry Division) fielded as timely as the Eighth was put into the field with added Corps coming on line as thing progress. The second Army will be further back likely centered near Allenstein. The battles will occur closer to the frontiers since Germany is no longer fighting a strategic defense in the East but moving to a strategic offense to break Russia. A certain amount of lure in will be conducted but part of how we get Tannenberg is the need to divide the Eighth between two Armies in detail and over all of Est Prussia, here each Army has its own enemy. I do not see enough units to fully encircle but the dismantling of both 1st and 2nd may be near complete. Effectively I would remove them from the war. Another Russian army should be as badly damaged if not destroyed by the Austrians. All rather rote.
I agree that the Russians are coming, but on two axis, not effectively coordinated, on thin logistic lines and meeting tactically superior German forces. If the battles open closer to the border there is better chance for the collapsing Russians to scatter and retreat into Russia, but as effective fighting units they are gone, able to mount some desperate defense at best as the Germans pursue, but it is Russia itself that will slow the Germans.
It is shades of gray, the Russians will be hitting the German forces they assumed from the beginning, some vague two Armies worth, the battles will unfold on bad ground, the Germans will prove most adept at fire and maneuver and all Russian weaknesses will be shown. Best case each General decided to save his army, worst case he tries to win points for honor, in the later Russia is losing those Armies. But Russia has vast territory to retreat into and is not effectively defeated, reeling from the defeats Congress Poland is poised to be overrun, the next big battles will be defensive and desperate, I give the Russians credit for bravery and the advantages of being on the defense. I think they suffer big bloody nose. I am uncertain if Nicholas can concede yet.
As you observe the West should be a mismatch in losses as Joffre doubles down in offensives, more so as Russia suffers, yet he will coalesce into a defense that is hard to break. France has effectively lost but can they admit it? Can we get peace feelers by Christmas or has Germany bitten the victory apple and gotten the disease? I like the scenario but the chorus of Germanwank is coming, their drums will try to get us back to Versailles.