The US Treasury should mint sets of ballot bills with 2 matching serial numbers for each set,

Each bill will have 2 blank boxes where you can write in your signature and choice of president.

Then send a set to each registered voter (tracked by serial number) who then returns the the second bill with their choice to the treasury department for auditing of the results.

Any contest can be resolved with a random pool verifying the second ballot bill against a pool of random voters.