What is the goal? Having fancy crypto or people being confident about elections?
If spreading the trust is the goal what makes you say "inefficient". It is orders of magnitude better then any crypto system.
The costliest item is counting by hand, so... don't. Use ballot scanning and counting machines and then implement a timely partial manual audit to demonstrate that the BMDs and BSCDs functioned correctly.
Automating any of the process is (imho) harmful to above.
While I’m a proponent of the paper process let’s not pretend it immediately means you can be confident about the election
With some abstract math and computers? Any real or imaginary issues are incomprehensible to most of the voters and concerns can be easily shooed away.