From: Cambridge, UK
Hmmm, I disagree here.
1) The Kaiser only wanted partial mob or Eastern mob, but the marshalling of troops was affected by railroad timetables. It was said by staff that once it was set in motion, it couldn't be changed.
2) The Russians definitely both mobilized quicker than expected and pushed into East Prussia with "what they had" there at the time. However, your assessment that Tannenburg was not a big victory, is incorrect. It was. It shattered an army. Granted the Russians had many more. It was also a morale victory for the Germans and a shock / morale dive for the Russians. The Germans big mistake was not realizing that they would roll a 6 on a d6 :-) and shifting "unneeded" troops from the W Front over.
3) It did NOT take 4 more years for the Germans to grind down the Russians. (It's lat for me, so I might have my facts off a bit, but...) Basically, after Tannenberg the Germans spent the rest of 1914 concentrating on the W Front. 1915 saw them switch to the E Front to help the Austrians, but 1916 saw them back concentrating on the W Front and France while the Russians did the Brusilov offensive. Early 1917 saw the Tsar abdicate. Pretty much from that time, the Russians didn't advance against the Germans at all. Ther was some action on vs. the Austrians, but pretty limited. It did take them almost a year to finally "collapse", but they were just tottering from that time.
So, if the Germans could have been able to hold vs. the W Allies and maybe just the French and to fully concentrate on the Russians, it would not have taken nearly so long. The difficulty of course is "holding against the W Allies". This can be done by a "modern" player, but without that hindsight and in that age of attack, attack, attack, I'm not sure that it could have been done. They didn't have the ability to trade space for time, especially in the Ruhr. I mean they freaked over the Russians invading East Prussia!
So, I think that it would be / should be hard to beat the Russians. Harder than many think, but easier than you asses. IMO the hardest part will be holding off the W Allies advance. That should be able to be mitigated by not invading Belgium.
Do I think that the Brits would have ultimately come in anyway, probably. But their big issue that made it a "just war" was the trampling of "little Belgium's" rights. Then to be honest without Britain whispering in Italy's ear, would THEY have come in so quickly? Don't know. So, not invading Belgium should push the entry of Britain and Italy back a variable, random amount of time.
There I combined two threads!
The Kaiser did order von Moltke to cancel the Schlieffen plan and prepare to deploy troops on the eastern front (On August 2nd) because he [the Kaiser] believed at the 11th hour the British would remain neutral if the Germans avoided violating belgian and luxembourg's neutrality. Motlke refused, but was still ordered to cancel/postpone the invasion of Luxemburg and Belgium was given an ultimatum later that day. So there was the possibility that the Germans could have launched and eastern attack. This was Moltke the elder's preference too was it not? Defeat the Russians then turn on the French? Germany's greatest advantage in that war was it's ability to transport troops from one front to the other with great speed.
Also remember that the Russians upset the Schlieffen plan, nut just Moltke the younger. Schlieffen gambled that the Russian mobilization would take 40 days before it could present a threat to the German frontier. But Russia attacked with it's standing army and did not wait until full mobilization to attack.
Also, remember, you players, that Tannenburg was not the defeat it seemed. The Russian army was still largely in tact, it took four years of attrition and shortages to really wear down the Russian military and the patience of the Russian people. I think, despite Germany's military superiority, an adventure focused on Russia could take more time than one might think. Beware of getting caught up in defeating Russia and it taking too long. Without pressure on the western allies, they'll be free to build up while the Central Powers are grinding themselves down on the eastern front. I think a two front war is unavoidable, and it has to be fought. Diverting Russian attention with smartly used Austrians is probably the safest strategy.