It would be a simple matter to get a small group of tech people into a room to design a state-of-the-art election system. You could determine requirements and parameters for a basic design in a day or two (a Washington committee would take a decade).
You could make it cheap, auditable, and essentially simultaneous. No one should know any state vote counts until they know 100% of the state vote counts. Or maybe no state releases any vote counts until all states are ready to release 100% of their vote counts.
Designing this would not be hard.
While we have our own troubles up here in the frozen North, our elections seem to have fewer problems for several reasons, some of them being:
All races use paper ballots.
NO results in a time zone are released until ALL the polls in that time zone are closed.
A minimum of two poll workers supervise the ballot boxes at all times.
Districts (ridings) are delineated by an impartial panel after census.