All you need is for each stack of ballots to be counted by two different people, neither of which know the count the other provided. A third person verifies these totals match, and if not, the stacks get tagged for recounting by two new counters in the same process.

It doesn't take long to hand count, and it's arguably faster than feeding ballots through a machine and dealing with accompanying errors. Significantly more trust. Even if both parties want to cheat the count, they have to come up with matching fraudulent totals making it difficult to pull off.