Best way to thin out alfalfa

I seeded a new pasture in Spring of 2015, took two cutting of hay off it, and turned the cattle out Spring of 2016.  

It is specifically a "grazing mix", made up of 20% grazing tolerant alfalfa, and a mix of several grasses and clover.  It looks more like 75% alfalfa.  I have been worried about bloat all year, but haven't had any problems until last night when two died.  Really upset as it is meant for grazing, and I am a small producer so I took a big hit.

Any ideas on how to thin out the alfalfa and get the grasses to take over?  

I rotationally graze so I can bring a few bales of dry hay every time I move them, but thats not solving the problem.  

Best way to thin out alfalfa