As you suggested, Cooperstown pitching is tough, since there’s no time limits (only run rule) and you can play so many games.
A lot of your planning depends on whether you think you will realistically go deep in bracket (save pitching) and how much pitching you have. Some teams just want to win as many games, either pool or bracket, as they can, and others expect to make a run for the championship.
We made the sweet 16 twice. The first time, we didn’t expect to do well and the second time we thought we could make the final 4 or have a shot at the finals (we did pick up a pitcher just for the tourney our second time).
Typically, I did as much research as I could on the teams we’d play. Then, I’d try to have my better pitchers pitch earlier in the tourney (and pull them in any game if we had a comfortable lead), so you’d have them fresher in bracket. In bracket, we just looked at our matchups and made the best guess we could as far as whether to throw one of our top pitchers in a given game. Nearly every team struggles with keeping things manageable for pitchers as far as pitch counts and innings…unless you’re a team who flies in or borrows pitchers for the tournament.
Personally, I would not schedule another tourney for a while after Cooperstown, since it does almost always stretch your pitching, and you can then get kids some rest.