I mean the premise already feels a bit absurd, but I'll play...

I'm not a vegan myself, and I don't really hang out in vegan spaces that much, so my answers may differ from your typical vegan, or not... who knows. But I suppose if the general goal is to preserve life where possible, then you should absolutely try to find some place for the animals to live out their days in peace. If we can manage to stuff them all in neat little boxes on the land we have now, I doubt it's some intractable problem. You don't have to let 'em run free and "out of control" per se, repurpose the land of the now defunct factory farms and slaughterhouses, build a number of sanctuaries all over the place, and plop 'em there. Of course, no one can possibly know all of the variables involved, so I'm not saying this is a well thought out solution, I'm just spitballing... but we're not exactly hurting for land, to my knowledge.

However, suppose I granted you:

Realistically the amount of livestock is not sustainable and they’d need to be culled in gargantuan numbers

Why would that necessitate this outcome?

And then you get the slaughter without the benefit of feeding billions of hungry people.

Veganism isn't some virus that physically prevents you from eating meat, and plenty of vegans have been meat eaters at some point in their lives. If it came down to it, I imagine there would be a steady supply of folks who would opt to revert temporarily instead of letting it go to waste. Vegans may disagree with me here, but I think it's certainly a more ethical choice if the animals are already dead, can't let the sacrifice be for nothing.

The vegan viewpoint on animals really just boils down to eliminating unnecessary suffering and death. Many are fine with the prospect of hunting, fishing, or raising livestock for food when there aren't other options (eg. environments with insufficient crop yields to feed everyone or infrastructure to get other food), the problem arises from the fact that those of us privileged enough to live in a land of abundance continue to needlessly slaughter. Do we need to eat? Of course. Do we need to kill things to do it? Fuck no.

All that said, I think a more realistic transition scenario would be something like the meat industry halting slaughter operations, exhausting their existing supply until either there are no animals left to kill, or there are a small enough quantity to where we can just yeet the rest onto some farms somewhere. Not that vegans would be entirely on board with that, being anti-slaughter and all, but it's at least a reduction in harm and a more believable way for things to play out... I think.