Your entire premise is based on there being a long complicated chain, which I think is a bit of a red herring. Voting happens in districts. The totals for those districts are already posted publicly. There's no need to validate the entire chain when the lowest level is already open and free to be audited by anyone. Additionally, for the districts I'm familiar with, polls are staffed by volunteers and anyone is free to stand around and watch the whole process.
A paper ballot system where local volunteers from the district count the votes at the polls in a manner that can be observed would absolutely work for the US. It would be pretty easy to just write down what the volunteers counted and then check later whether that matched up with the nationally posted numbers. No long chain to decipher, no obscure software to worry about. And, as a bonus, there are places where this is already done this way, so really nothing needs to change policy wise (other than eliminating the other methods).
A paper ballot system where local volunteers from the district count the votes at the polls in a manner that can be observed would absolutely work for the US. It would be pretty easy to just write down what the volunteers counted and then check later whether that matched up with the nationally posted numbers. No long chain to decipher, no obscure software to worry about. And, as a bonus, there are places where this is already done this way, so really nothing needs to change policy wise (other than eliminating the other methods).