What I'd like to see is a way any voter could verify, after the election and in a way that could not be falsified, that their vote was actually counted as they intended.

I know cryptologists were working on this problem several decades ago but I haven't kept up with that research.

Here's something about it: End-to-end auditable voting systems.

It would remove any credible doubt about the integrity of the system. I think we could all use that about now.