(Having some trouble replying to specific people, so thanks to all for your help. Here's the outcome...)
Both grey tanks will now drain properly thru the garden hose. I don't know for sure what worked, but I know it wasn't the fault of the hose.
The roof vent caps looked fine. I don't think anything could have gotten in them. It seems alternating the Kitchen/Shower valves somehow allowed the replacement air into the system. It's really the only thing I did that could have had an effect.
Again, thanks to all, especially those who helped me understand the inner workings of the holding tank systems.
