> In a large election it is a big challenge to ensure that independent observers from all parties are present every place someone could potentially tamper with ballots in storage or in transit between the time they are cast (especially in jurisdictions where polls are open a long time) and are counted and the count is folded into the overall total.

It's actually pretty easy: Count the ballots at the polling place immediately after the polls close. That leaves no opportunity to leave them unguarded. Publish the results of each place so everyone can reproduce how they are summed up.