That's a good tip, but I'm not sure the stuff I'm seeing on the wrestling sites is what I was talking about. I think this wrestling stuff is more powerful, as it is claiming to completely disinfect surfaces and I'm also seeing the word 'detergent'. I just started looking though, and haven't seen ingredient lists on any of them yet.
Actually disinfecting the mats is probably a good idea, but what we used was more along the lines of the pet odor remover solutions. I just found another type of product that claims to be better than enzymes at removing smells, designed for cat pee:
http://www.forceoutproducts.com/cat_odors/index.htm
Enzymes are almost certainly inert and harmless once the treatment is over. I saw the MSDS data sheet on a peppermint enzyme soap and OSHA declared it completely harmless. The ad claims this cat thing is even more benign. In general, if toxicity to kids and adults is an issue, I think one of these biological cleaners is going to be better than caustic chemicals like bleach, detergents, or other disinfectants. The problem is that I think these only work on smells.
Since starting this thread, I talked to someone who had great success cleaning their mat cover by taking it outside and spraying it with a pressure-washer, using just water. Although removing and replacing the cover would be a pain, this sounds like the best solution to me for stains.