I'm looking for Heroes players who play quickly (1-2 minutes per turn, but WITHOUT a timer!).

I played a lot against people who would literally run around for 1-2 minutes and then immediately pass their turn (with normal settings, SOD is 6 minutes, TE is 4000+400). Judging by their save files, all these people played very poorly and always lost without a chance. If you're playing against a person, you should only play to win, and that requires more time for both strategy and battles.
However, if you were to create a separate tournament with a very fast time control, promote such a tournament effectively, and manage to invite strong and respected players, that would be a different story!