I'm fairly sure that that text doesn't detail an army size specifically in order to do anything- it's just the army sizes in the Strategikon are assumed, rather than proscribed. I could be wrong though, it's been a while since I've read it. Realistically, though, small armies do tend to lose battles- it's just our sources like to talk about a handful of heroic figures mowing down legions of cowardly enemies.
Well, if large armies were better, I think we'd see more about maintaining large forces and less about fighting smarter, not harder.
And speaking in general, well lead armies tend to win battles, not merely large ones, though.
Not so much handfuls of heroic fighters vs. legions of ninnies as - for example - Stonewall Jackson having fewer troops than the total Federal troops in and around the Shenandoah Valley.
That sort of thing is a serious problem given the logistical hell of maintaining that many men in one place - I strongly suspect anyone would have broken it into more manageable chunks (which is not saying that they wouldn't be enough if well lead, but I keep emphasizing leadership because that's what the Vandals had in their favor OTL when they lost - and didn't when they lost to Beli).
As for the East being willing to prop up a Western state- I think the efforts of 425, 440, 468, 533 and 551 show quite conclusively that the political will and ideology was there. In any case, the East does not inevitably hold the whip hand here. Recall that Constantine and later Heraclius conquered the Eastern Empire from the West, not vice versa.
And the political will and ideology being there for a while is not the same as it always being there. I mean, let's say the East maintains it for as long as OTL plus change (call it up to ~600). What then? At some point, it's going to have other interests and commitments - assuming the twenty-sixty-years war is butterflied, there's still gonna be something at some point.
As for the whip hand: Constantine was a century and a half earlier and Heraclius with support for Phocas being . . . weakened.
I'm not sure the West has any leverage it can put on the East.
So what this all boils to is: I think the West might have a chance. But it's only a chance.
Good management and good generalship can make dent into things, but the days when Cannae level defeats looked worse than they really were are gone in the West by this point.