for now I've just stopped growing it. lol. I think it's more the heat than the humidity for the mold/mildew/slimey grossness though. Everything I've read says that fodder grows best in a cool environment. I think what I want to this fall is try to set up some racks under the florescent lights in the basement, it stays cool there year round, and I can set up an automatic waterer. If you're doing more than a couple small trays that seems to be the way to go. Not too expensive to build yourself from a basic pump and some PVC, and takes the trouble out of watering etc. Then all you have to do is go down once or twice a day, change the water (which gets starchy. no big deal for me because we have an open drain in our basement) and swap the trays around/start soaking the new seeds for the empty trays. There's some plans for them earlier in this thread, and you can find a ton of them online. You can even use a basic flood table type setup as in aquaponics.
for me I might be tempted to mix the wheat and barley and offer both. I think getting a diversity of food types is good for any animals (including humans!).