For #2, what if you relax the "no tactical voting" requirement to say that voters cannot predict how to vote tactically unless they have an impractically large quantity of information about other voters?
This is the insight. Proving "tactical voting is always theoretically possible" sounds bad, until you realize that there exist systems where tactical voting requires not only nearly perfect information about every other voters exact preferences ahead of time, but also solving cryptographically hard problems
I think I'd be satisfied with that. Or ideally, "given attainable information, an honest vote is the most likely to make the output most agree with me."