I don't like the 3-batter minimum. Too arbitrary, and too many unintended consequences would arise. Don't take more strategy out of the game, nor add incentives for subterfuge ("hey Meat, tell the ump, your shoulder hurts"). The complaint isn't that it's a different pitcher, but that the pitching change takes time. So, address that. Make the relief pitcher come to the dugout on his own time (maybe some logistics need to be worked out, given where bullpens sit in some ballparks), so that it's a short stroll from dugout to mound. Soccer and basketball require substitutes to wait at a designated spot, after all. And then when he takes the mound, he just starts pitching - he spent all that time warming up, right? The guy he replaced didn't throw warmup pitches between batters, the new guy shouldn't either. Warmup patterns in the bullpen may need to change, but they'll figure it out.