Hating to win is one thing, but the rules aren't meaningless. When you join a league you have to play by the rules. You're just not paying attention. Do you hate to lose enough to do something about it?
If your starters suck then you'd be losing pitching anyway. 9er Fan has the way of it. You need to figure out how to win within these rules, especially if the others haven't caught on yet.
IMO keep your most reliable closer or two -- take the one cat, and help out in ERA. Improve your SP as much as possible.
I suggest forgetting about the 2 start losers. Reliable pitchers should give you S and ERA, a shot at W, and sometimes even K. Punt IP instead and use quality over quantity. I could be wrong about this, but it feels right, I like it and I'd give it a shot. Go for it!
I think IP as a cat is viable as long as there are additional cats that require some quality over quantity, e.g. WHIP, L, HRs, BB.
I think I'd be as surprised as you were by the strategies employed against you. However, I also love challenges and coming from behind, so I'd be doing some thinking about how to turn things around.