Dealing with estreme splits teams

Periodically I see strong opposing teams using platoons with extreme splits all over the place. Shano, Duncan, Mercer, etc paired with a bunch of 8-9R bats like Brown. How do you set up a team to beat that strategy without making the team vulnerable to teams with more conventional lineups? This time I've tried a "thick" bullpen with lots of cheap extreme relievers, trying to force the pinch hitters and then, HAL permitting, turning them around. Thoughts? Thanks for any advice.

One key element to using the cheap extreme relievers in this situation is to have enough of them. Hal wants to know he has more arms available in the pen, or he'll leave the lefty in to face a righty.