Nothing about the US system is particularly geared to prevent double voting.
I get that you don’t have a federal register (something you should really fix tbh) but requiring manual registration when you could, oh idk, simply register people when they are born and then later automatically provide them a unique ID they can vote with? (I’m not even talking a government ID for the purposes of identifying yourself to law enforcement and stuff, I’m talking even just a voter ID for the sake of voting only)
Then have part of the number in that ID identify the state you’re from if you want to prevent crossing borders to double vote (kinda like how credit card numbers have that info on them).
It’s what they do here anyway, I’ve had an ID since I was like 4, and it’s with that document that I and everyone else votes.
Though I know the US is probably too anti-democratic for this and none of the parties in power want to change jack.