This is all pretty solid advice. let me add what I do.
Heavy lifting -- mostly pulls (love rack pulls these days and rows) since combat athletes tend to stay stuck in trunk flexion (that's the safest position to fight in) as well as some pushes in various planes, such as overheads and bench. I tend to favor dumbbells over bars just because I think you can't get nearly enough stability work. The single biggest difference to my training I have found is to focus mostly on posterior chain work outside of martial arts training.
Agility/stability training - You cannot be mobile without having good stability. This means things like planks, side bridges &c. and isometrics (e.g., do a pull-up and stay stuck at the top for 5 seconds per rep.) I mix these up with footwork drills (includes combos with rolls, falls & sprawls as well as floorwork) and sprints. Oh, and fall in love with ITYs as well as face pulls. These help overcome the major training imbalance of always punching/hitting things. Swing tabatas are a good ending to this workout. Do them right though and don't hurt your back or shoulders.
I alternate these workouts and add cardio in several times a week. This takes any of several different forms, such as jogging, biking or swimming. Oh, and I also just took up rock climbing a couple of months ago which is pretty good too...
FWIW I've been doing this pretty much for the last 6 months and dropped a bit of weight. Imagine my surprise to find that my last bodyfat test I had slid down from around 12% to slightly less than 8% without really trying. And yes, I look like an android. :o)