However, I still miss a clear casus belli, if both Belgium and France are not attacked by Germany. Morally speaking, it is a huge difference to go to war to defend a country that is under attack, or to go to war to support a country that chooses to attack. In any case, a German invasion of Luxembourg was not enough, as
this source clearly shows:
Diplomacy isn't a Paradox Interactive game, a "real" casus belli isn't needed. No one in the Cabinet cared about Belgium in the slightest either, certainly not Grey, but he played that card for all it was worth to win support for intervention. All the formulation that the UK needs is that Germany is an "aggressor nation" who has already occupied "tiny Luxembourg" and aims to establish Hunnic hegemony over Eastern Europe.
You're conflating how the war is advertised and justified with how the decision to go to war is made. IOTL Britain's decision to go to war was made by cabinet and Party power politics as well as the logic of the imperial and continental balance of power, which impelled the Asquith cabinet to oppose Germany or else face its complete collapse and mobilized the majority of the cabinet to support that platform. Belgium was an advertised justification but not the root cause of the UK's intervention.
"Naval war only" is a rather naive thought. But with this "promise" the warmongers may succeed in getting Britain into the war. However, British soldiers will soon be deployed against the Ottoman Empire and later on the Macedonian front and in Italy. This creates a full war effort, which will exhaust Britain completely, just like in OTL.
The UK was never exhausted IOTL, and certainly wouldn't be from a much smaller overseas commitment ITTL. I completely agree with you however that in the long run "naval war only" is a useless formulation. However, it had immense appeal even among anti-intervention Liberals pre-Belgium as a way to avoid a full continental commitment. Only with the benefit of hindsight (Ottomans and Italy entering the war, Serbia collapsing, etc.) does the ever-expanding nature of WW1 become obvious.
In any case, I don't understand what the British 'fear' is that Germany will dominate central Europe. Jealousy maybe? The German focus on "mitteleuropa" is not a threat to the British Empire. In 1914 Germany was already economically the strongest country in Europe, and it has remained so to this day, despite the loss of two world wars and the loss of a third of its territory. Britain has lost its Empire, so who actually won? A British war entry does not change the geography. Germany remains a large country in the center of Europe, with a large population and a large industry. What's the point for the British to fight against that?
The two powers had had intense naval competition for some time, especially as Germany expanded its colonial possessions, and Germany's constant butting heads with France overseas in 1905 and 1911 were worrisome prospects. Germany's increasing influence in the Ottoman Empire/Persia didn't help.
Many politicians at the time were gripped by a logic of empire and imperial competition which impelled them to see the world in ways which seem absurd to use nowadays. Nonetheless, if you assume
prima facie that maintaining a global empire is good and necessary opposing Germany, even in a bloody continental war, seems sensible.
Indeed, I mainly use Wikipedia and other sites as a source. I should buy that book of Zuber... It is also a bit confusing to which version of which deployment plan is referred to. The four plans were updated annually I understand. In any case, given Germany's fear of a French attack, it is out of the question that Germany will send more than half of its army east. "Aufmarsch I Ost" is actually more obvious. Or an "Aufmarsch II Ost" with the number of divisions of "Aufmarsch I Ost". That means 5 armies to defend the west and 3 armies to attack Russia, according to your own source.
I must confess that I actually misread by own source. Aufmarsch I East/East and West (It was named both) never had the 3 armies East 5 West formulation you've mentioned. Aufmarsch I East deployed 12-13 divisions East and the remainder West. Only the "Great Eastern Deployment", Aufmarsch II Ost, involved a substantial commitment to the East (43 divisions East, 32 West, 10 in reserve) and would be the only plan followed (Moltke the Younger himself is the one who came up with it).
You can claim credit that your formulation of 50% West 50% East was correct, as with the 10 reserve divisions deployed West as they likely would be that's Germany's operational set up. But I've seen no smaller offensively-oriented Eastern commitment than that.
If the British warmongers did indeed get their way, I expect the Great War to end about the same as OTL. The Industry in Northern France remains intact in this TL, but the iron ore deposits around Longwy and Briey are in the middle of a war zone and are unusable. France will be able to produce some more weapons and ammunition, but I do not expect any decisive success. By 1916, France will be able to launch a major offensive, i.e., a "Battle of Metz" as a counterpart to the OTL Battle of Verdun. Germany will bleed, but France will also bleed itself to death. French troops will be supplemented by British troops, and perhaps American troops later on? Perhaps the Macedonian and Italian fronts will also play a greater role in this TL.
You really haven't shown how or why Longwy-Briey will be occupied at all. The entirety of the first wave of fighting, and the majority of both side's divisions, will be between Metz and Strasburg, very distant from the iron ore West of the Moselle.
The French would deploy 3 of their active armies (4th, 2nd, and 1st, West to East) between the Moselle and the Vosges attacking North toward Lorraine as well as part of the 3rd Army, which would invest Metz and cover 4th Army's left wing with 3 corps. In total that's 28 active divisions between Metz and the Bruche, with another 10 reserve divisions in the rear. 5th Army would attack between Metz and the Luxembourg border along with part of 3rd army, 12 divisions total with another 5 in reserve, only entering Luxembourg if the Germans did first. Plan XVII once again for reference:
The German initial mobilization would be 5th Army with 5 corps (10 divisions) from Metz to the Belgian border, 6th and 7th Armies with 10Corps between Metz and Strasbourg, and 2 Corps in Upper Alsace around Mulhouse to await the arrival of the Italian Army. The German intention was to remain flexible and concentrate the majority of its forces against the main French blow. Luxembourg would be invaded, with VII Corps occupying the Moselle, Our, and Sur bridges leading into the country.
The French will have superior numbers West of the Moselle (16 French divisions vs 6-8 German), will be halted along the river and somewhere in Luxembourg, and from there this sideshow theater will be inactive as both side's reserves are consumed in the fighting further East. There's no reason for Germany to commit its meagre forces crossing the Moselle to seize what in 1914 was a wholly unimportant region in their calculus, nor for the French not to reinforce and resist stiffly against German attempts to counterattack across the border should they emerge. IOTL Germany attacked toward Nancy and was driven back across the border by overall weaker French forces. If the French Army is much stronger, there no reason to believe the final frontline when both sides are exhausted won't be well within German territory.
There's actually no reason for Germany to not withdraw behind its fortifications at all if it has initially defeated but not destroyed the French Army. Otherwise it simply invites defeat in the open by a much larger enemy army which still has ample reserves of men and material.
Starting from a hypothesis ("An Eastern Deployment works great for Germany") and then working backward from there to mold facts to the narrative rather than considering potential alternatives ("A strong and unmolested French Army is very dangerous" and "Germany has no plans or ability to occupy or disable French industry") isn't a good way to consider how a TL unfolds.