I would set up each reporting unit (precint/causaus site) with their own sheet. There are probably only 5-10 officials per site that should even have edit access, maybe less, like only secretaries?

Make a nice formatted layout specific to that year. People feel pretty comfortable in excel-like spreadsheets/forms.

Then at the state level, since you have permission to all the sheets, its simple to aggregates all the sheet data

It's not some wiz-bang branded app with fancy animations, but its piggybacking on a very robust spreadsheet system that many people have some experience/intuition with.