You might be underestimating war-weariness a tad, Homer. While there were many volunteers in the Freikorps, there were probably just as many Spartacists who melted into the working classes when the 1919 uprising was crushed. If there was renewed fighting and these Freikorps were sent to the front, who would be left behind to crush the workers? It would be utter chaos, with rival militias and all that malarkey.
This is something I concluded: the Russian October Revolution was only possible because Russia was still fighting the war when the liberals held power. While in Germany in 1919 the soldiers were all back home ready and willing to crush the Communists, in Russia in 1917 all the soldiers were at the front suffering severe morale problems. If Germany had continued to fight the war after the Weimar Republic came to power, then the Petrograd uprising would have undoubtedly repeated itself in Moscow. This is what makes the October Revolution such an unmistakebly aberrant event, since city-based uprisings rarely last long against the might of the military. All the other major Communist revolutions of the 20th century were rural in support.
In launching a great war less than two years after settling the greatest war in human history, you successfully turn the exception into the norm. Everyone was exhausted after 4 years of unremitting torture, buried under war debts, putting down nationalist revolts in places that had gone untended during the years of struggle, dealing with millions upon millions of walking wounded and emphatically without American support (the US senate had recently rejected the Treaty of Versailles and Wilson's support was on the ropes. If he ever brought up the possibility of intervening such a possibility would be quickly quashed). France and Britain in particular were utterly shattered, as they didn't consider war to be a cathartic experience like many Germans did. And if by this stage the Germans had staged a huge revolt to bring about an end to fighting, imagine how the French and British felt. And of course the Italians are still peeved about not getting their just rewards, so joining in the other great powers in a crusade may just get the two-fingered salute from the population.
With Romania/Finland et al I'm not even sure they'd be terribly enthusiastic about joining in the crusade. They'd join more out of terror than enthusiasm, more likely. Out of all the potential candidates for allies in the crusade I can only envisage the Japanese greeting it with triumphalism. And the track record of nations 'picking up support on the march', if you look back at history, is a tad sketchy at best. The Poles may join in, but I'm not too sure about Ukrainians greeting Romanian conquerers with garlands of flowers. These people have been pawns of greater powers for longer than they can remember, and quite frankly not having a Polish state causes the western powers fewer headaches. The relationship with the 'liberated peoples' is bound to sour eventually.
Remember, although the bourgeois elite of the west was terrified of the reds, to large masses of the population the Russian Bolsheviks were heroes. The 'red tide' of 1919 is testament to that. If the Russians publicly state that they'd rather have a peaceful settlement then the workers of the west are going to be very ambivalent about their nation's war effort. What able-bodied people there are left are being dispatched to the front, leaving behind a rabble of malcontents to shore up industry. It's a recipe for revolt if ever I saw one. This 'great alliance of democracy' is good propaganda, but hardly feasible.
And, raising the question asked in an earlier post, what about the United States? With Europe descending into chaos and America staying neutral, will there be a new influx of refugees? And how does this effect the roaring twenties?