Using generator exhaust is inviting overheating the tank. I’ve been around one when the relief valve pops, and that’s a big fire waiting for a spark. It doesn’t take a lot of heat - maybe 30 watts - to keep the pressure up. They make tank wrap heaters specifically for this purpose. But I needed power (this was during one of California’s infamous “Public Safety Power Shutoffs” used to avoid wildfires). So I used what I had; a washtub and water.
The standard 20# tank has only one safety device - an overfill protection mechanism that prevents filling the tank more than 80%. The propane regulator for portable propane appliances is where the flow limiting device is located. That heavily limits the flow of propane if it detects insufficient backpressure on the outlet side of the regulator when initially pressurizing it (turning on the tank valve).
I have no issue with the 500 gallon tank. It has plenty of surface area in contact with the propane and good air circulation around the entire tank.