LOL, that's EXACTLY what I've been thinking!
I'll add the other part, which isn't actually my idea: There are two things to print: your ballot, and your receipt.
Your receipt has your voter ID and the hash that you mentioned. You can take that home and check it.
Your ballot would have a legible compilation of your votes, so that you can look at it and confirm it is correct. And, it would have a bar code that encodes all the votes.
The bar code on the ballot is then scanned (preferably at the polling place), and only the hash needs to be retained, so that it can be uploaded and checked online. Of course, the paper ballot is retained. And, a recount could be performed by re-scanning the ballots, with the hash preventing duplicates. Any discrepancies would be easy to spot, and provide evidence of where the fraud occurred.
Or, do you think the entire (encoded) ballot should be retained? That would provide the ability to back out a ballot that is found to be fraudulent. But, it would also give someone the ability to discern the contents of a ballot: back it out and look at how the totals changed.
I'll add a couple of other things for consideration: the ballot should be signed with the voting machine's private key. That provides an audit trail back to the specific voting machine. If a bunch of bogus votes are injected into the count, their private key wouldn't be valid.
The voting machine could be relatively simple: a touchscreen and a printer with a Raspberry Pi (a complete computer for $35).
I like the ideas but do have one caution. The receipt needs to be done in such a way as to prevent someone from using that receipt to see what votes were cast. If that were allowed, it would potentially allow thugs to force a voter to reveal how they voted. Think union thugs coming to a person’s home and taking the receipt and “verifying” their votes or bosses demanding the employee’s hash or be fired.