Instead of bleach, you might try hydrogen peroxide. If nothing else, it will be easier to clean up. You'd want the 35% concentration sold in health food stores, which is used to disinfect seeds and home grown sprouts. You'll dilute that of course, but it's much more efficient than trying to use the 3% stuff from drugstores. If you can't get that, a drugstore should have or be able to get 6% hydrogen peroxide, aka 20 volume. It's for bleaching hair, but at twice the strength will work better on your slime problem.
It's a powerful oxidizer, just as bleach, Excel and potassium permanganate are, but is easier and a bit safer to use I think, and no bleach smell. No need to treat for it afterward, a simple rinse is all you'd need.
Good luck. I've never seen wood grow that much gunk.. though my snails ate anything that did grow, and never heard of slime like you have. It must be hell after all this time.