Well if you're doing strength training many of the BW exercises in class should become easier to the point where they are mainly endurance exercises.
I don't know how your MA classes are structured, but when I was regularly doing MMA on top of weights there was zero need to run. Doing 3-5 minute BJJ rounds was harder than any cardio I could come up with anyways
__________________
"Only those who will risk going too far can possibly find out how far one can go." -- T.S. Eliot
"We are what we repeatedly do. Excellence, therefore, is not an act, but a habit."-- Aristotle
"Losers make excuses, winners make it happen!"
http://www.thepensiveprogrammer.com/