Going to jump in here with my worthless two cents. Probably quoting people...
Round 1 can be a bit dry right now, but it's fine if it moves faster. Pacing and format are two different animals and that'll get improved with more run-throughs.
Round 2, simplify the rule: "You may never pass on two consecutive questions". It still creates the possibility for an all-play while also not forcing the obvious tactic of passing when an opponent has four strikes and you don't. (And obvious tactic was obvious to your contestants.) It's a simpler rule than what you have right now (and you admittedly want simpler rules). It also speeds up the game since players who pass have their decisions made for them on the following question. If you want to add meat to the decision making without adding more rules on top of that, have a "NEXT" box to show what the category will be for the following question that they'll be forced to play if they pass this one.
Round 3 is, in fact, the previously mentioned bread sandwich. Here's your fix: There's a category board, one question in each category. Have a general knowledge toss-up. The toss-up isn't worth a strike. Instead, the toss-up winner can choose to play a category or can force the opponent to play a category of the toss-up winner's choice. This also addresses Travis' concern about being able to give a strike to an opponent who can do nothing about it. This
also increases the value of knowledge gained about your opponents' strengths and weaknesses earlier in the game, which can only be a good thing.
While the bonus is straightforward, the win condition is creative and interesting. I understand why you chose it. It does create the side effect, though, that someone who did well in the first three rounds wins less than someone who just survived to the bonus. This is easily fixed by changing the total win to a flat amount though.
Some folks might have a problem with the advantages carried by one player over another from round to round. I don't. I view it as the strength of your game, and it's the kind of thing that's missing from too many formats.
Round two is clever but why wouldn't a savvy player just pass every time?
Because if everyone tries to do that, the next question is an automatic must-play for everyone, at which point you either get the question right or get a strike. The optimal strategy isn't to duck every question; if anything you want to play as many questions as you feel confident in playing because that accelerates the round (more situations where both your opponents get a strike as opposed to just one of them).
No, it's not. Because if you're the only one who plays a question, then the only one who can get a strike is you. If you were the only one who played a question, and getting it right meant your opponents get strikes, then it might be different. As it is, you can be penalized for playing and your opponents rewarded for doing nothing.
I get that there's a bit of a Challengers vibe there, but on that show, everyone had to play on every category in some way. The math works way different here.