I hear ya on the mat time. I definitely plan on spending tons of time there to work on the techniques and such since that's where the real power is, but I do enjoy supplementing with weights. It's so great to get that perfect takedown, throw, strike, wehatever and feel the effortlessness was it works, then the added power of muscle built by time at the weightpile...maybe it's just me... I dunno.
I also want to build my core more to avoid injury from getting slammed to the mat all the time. Getting your spine jarred like that ain't no kind of fun...well maybe...
As for the MMA aspect of your question, I did that for a while but honestly, it's just not my thing anymore. I'm more interested in the throwing and unbalancing, now than the punching and grappling. However, I will say that the Brazilian playing definitely helped me plow through some less ground experienced Judo players this morning...that was fun
P.S. I do remember how tight and cut up my abs were when I was doing traditional Japanese JuJutsu...great for the obliques BTW.