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.
One very good way is to get their followers into the actual collecting and counting process with independent observers in a way that they can't just cheat, but in a way that they can also perceive whether the other side cheats.
And you do that through all the levels of the election process. That is incredibly inefficient compared to everybody pressing a button on an app in their phone, but it gives you something that the phone app cannot: the loser party will know to a certain degree that their loss was legitimate (if the process was carried out correctly).
While with the phone app, who knows? Not even an expert that wrote the code of the app could guarantee that everything went without interference. And even if there wasn't any interference and we can mathematically guarantee it: the problem is that people need to believe it. And that means trusting experts, which may or may not be biased.
Meanwhile with the paper ballot the system is simple enough for most followers of each party to intuitively grasp whether something fishy happened. They just need to make sure every vote is counted and none discarded.
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.
It definitely didn’t help with trust even though I think German democracy is still mostly fine and something worth fighting for- but I guess that’s a different topic