I think we should return back to paper ballots. When there are witnesses to elections, I don't think any of them are qualified to judge if an election has been done in a honest fashion. This would require experts on the voting equipment where they can guarantee that it has not been tampered with and that is too high a burden and something that complex can not be trusted.
I don't think you should leave without (at least seeing) proof that your votes were properly and accurately recorded.
If that means that you have to be given a "receipt" with the names of those you voted for on it, well, so be it. It isn't like your name and/or any other personally identifiable information would be on it -- just the minimal details needed to achieve the singlemost important purpose: verification.
The proof would be a paper ballot that you turn in. Your actual vote.
A printed receipt, from an electronic polling place could just as easily be placed in a secure box prior to leaving.
It's amusing watching "ballot selfies" issue too -- it seems that folks just don't understand how important it is not allowing any coercive force influencing or verifying your vote.
Now imagine cults and other groups that pressure their members into producing those receipts with the correct candidate on them... or else.
One way it's done is that after entering your choices on touchscreen, you see the printed receipt through a glass window, and then it's stored so a recount can be done if necessary.
However, an electrically scanned paper ballot seems a lot simpler.
I actually believe this is actually the best possible situation.
The voting machine should print a clear, unambiguous, ballot and on-screen tell you to verify it before you officially "cast" your vote. "If the ballot below does not represent your choices, please click <HERE> to request an attendant."
I'm thinking of this more as having printers that print out an unambiguous completed ballot and less as voting machines that "also print out a copy".