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.