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> as long as the vote can be replayed/recounted without ambiguity.

Isn't this the core problem with most electronic voting as currently implemented in the US? I mean, that no such guarantee exists?

That's traditionally been the problem with voting machines: a "recount" just re-read some tally.

Combine this with voting machine companies being opaque, not recognizing obvious flaws and their executives promising to deliver states to particular candidates (https://www.commondreams.org/headlines03/0828-08.htm), and you begin to feel that all the suspicion is justified.

It needs a paper record, this needs to be the source of truth.

Not just a paper record. A hand marked paper record. If it doesn't go through a computer first it can't be altered. There are several states that do it this way. It's a "Scantron" style ballot. Fill in the vote, run it through a tally machine and save the ballot. The tally machines could be messed with, but if there is evidence of tampering with the tally there is always the authentic original ballot.

Yes!

If you've got a paper record, just use that instead of the machines.

Machines just add more opportunities for fraud.