First off, big ups to you for donating your time and effort to host a tournament. No matter what rules you go with, I wish you luck.
Forced diversity isn't really diversity. It's the same reason we allow two of most classes in 6v6 game-play. Sure, you could FORCE a limit of one, FORCING teams to run snipers or heavies... but that's dumb. I'd elaborate, but there are already like 800 threads on this forum concerning that topic. Also, see sigafoo cup.
Again, skill in TF2 isn't limited solely to Scout and Soldier. That's extremely narrow-minded, and if we aren't willing to experiment I don't see the scene growing in any significant way.
It kinda is. You don't have to be a pyro main to be a "good" pyro.
As for a pyro vs pyro 1v1, what is that really? Two pyros running around with minimal movement shotgunning eachother?
What about an engie 1v1? Same thing but smaller hitboxes.
What about a sniper 1v1? Baitscoping.
Medic? ... degroot keep?
You talk about how stale watching the 6s classes mge would get, but none of those other fights sound very interesting or skill intensive. At best you might get someone vastly superior to another player throw the second round on purpose, so he can avoid a "ditto" match in the third game, and go engie vs soldier or med vs soldier just to be a dick. That's about the most entertainment I could see out of your proposed ruleset.
Like I said, it's your tourney, and I don't even play this game, so do what you want - you have that right, and rightfully so (no pun intended) - but there's a reason basically everyone is rolling their eyes at the idea of forced classes.