I don't think the non expert voters not understanding the security is that big of a concern. Assuming that the security undisputed amongts experts, the media could convey this to the general population (absent some well supported opposition like climate science faces). At this point, the security points that need to be conveyed to the voters are relatively simple:

1) The receipt you are given may be used to confirm that your vote was correctly counted. Here is a list of websites/programs that you can use to verify your receipt.

2) It is impossible to use your receipt to prove to a third party how you voted.

If we could get major news source (New York Times, CNN, Fox News, etc) to publish their own tools for (1), then I suspect that should give a fair amount of credibility for the general public.

The problem I see is that any technical system of plausible deniability I can think of, would require that a voter is able to forge a receipt that would correctly validate as the incorrect vote. Otherwise, if an attacker wanted to verify that Alice voted Democrat, he could assume she voted Republican and attempt to verify the receipt.

How could it prove to you that your vote was included in the correct total without also being able to transfer that knowledge to a third party that is right there with you?

Say A and B were the options. Anywhere you take the receipt to verify it has to then display if it counted towards A or towards B. Someone there with you could then see which it confirms.

Inside the voting booth you pick an identified ballot and are given a zero knowledge proof that it corresponds to the candidate you want. The fact that it's a zero knowledge proof prevents you from using it to convince other people.

The video I linked has a good example where you get 1000 envelopes all claiming to contain "Obama", so you open and verify 999 of them at random and use that as evidence that the one you didn't unseal is good. You can't then use that to convince a third party, because they didn't get to pick the envelope to not open. The video also addresses lots of other security issues; you should watch it.

My concern would be in proving that the envelope you didn't open is the same one that made it into the final count. If you have no more connection with it after you leave the booth, you can not verify that the letter wasn't tampered with (and also no one can coerce you into showing who you voted for). Any way that lets you verify that the last envelope wasn't tampered with would also let some third party see who you voted for.

Anything the machine electronically presents you with can be modified on a compromised machine, while physical printout that can be used later to verify will either be unable to prove that your vote wasn't switched (though it can prove that your vote was counted) or it will be able to prove you did vote for who you choose, the latter case meaning that a third party can then use this to know who you voted for.

You're attacking the parts of the analogy that don't apply to the actual cryptography. Best way to see how they get around the issue you're talking about is to watch the video.