Does it seem reasonably likely to you that PoS could increase the proportion of computational resources that attackers would need, provided that the attackers control a low enough proportion of the tokens?

Intuitively, I'd say no. I can't see how you can ever prevent a '51%' attack (that is, 51% of compute power). No matter how many coins you own, the attackers can validate their own holdings and disavow the honest stakeholders.

At first glance, it seems to be a solvable problem because you can try to put obstacles in place that punish attackers (e.g. fining PoS attackers who generate 'false' results). But you cannot make these inducements to honesty bite, the attackers can happily keep churning out false results until they take over.

The problem is worsened because PoS is meant to save wasteful power usage. Honest participants are not likely to dedicate vast computational resources to it, while the attackers will be strongly motivated to do so. The end result seems likely to be an arms race, leading to an effective slide back to PoW, just with added complexity.