The solution seems simple at first glance; scrap the entire voting system, scrap the entire fundraising system, and whichever candidate receives more individual $1 donations via check or money order wins. You can vote a dollar to as many candidates as you want but your federal tax return for that year is only getting a single $1 election credit. You could require the candidates to declare to the IRS each $1 contributor which makes election fraud also a form of income tax fraud.
Certainly, our financial marketplaces and clearinghouses at their absolute worst are more trustworthy and reliable than our evoting systems at their absolute best. And the additional infrastructure to transfer a hundred million bucks every four years is utterly trivial (well, more often due to primaries and midterm elections, but its still a drop in the bucket ...)
The anonymity emperor has no clothes, anyway. Thanks to the miracle of modern technology everyone who matters already knows exactly who you voted for and your complete financial life, you're just plausibly deniable on an individual basis against some non-state opfor some of the time. May as well face reality and make all votes part of the public financial record. Sure, it sucks. But better to face a reality you don't like, than to live in a fantasy world of completely broken anonymity. Living a lie means you'll slip up and the consequences of the slip up are likely worse than the lack of anonymity itself.
No, if you don't trust that your paper vote is actually counted you could stay in the election hall all day, watch the counting, check the when the results are transmitted. You don't have any comparable option with e-voting.