Funny you should mention this. I just took mine to a jam last weekend in a case that fits perfectly, although I don't have the MKIII (I've got the original 424).
I'm using an old electric typewriter case. I layed down a cut-to-size piece of carpet padding on the bottom and rear, and I lay another pad on top. There's even room for my power supply and a couple of tapes.
It fits snugly and offers quite a bit of protection. Look around for something like that, or ask at an office equipment place if they've got anything old in the basement that might do the same for you.
Tascam accessories, should they exist, should be listed on the official website.
