(Typing in capitals makes it kind of hard to read.)
I had a transfer switch on my MH with a bad relay also. And the previous owner had changed it some time before I got it, so that replacement didn't last long. When I first started the generator after buying the rig, I discovered very high voltage - caused by the generator's need for servicing. It was up to about 160 VAC. That's probablly what wiped out the relay coil (and some other things like fridge and water heater control boards, which I had to also replace)
Anyway, I decided to buy a replacement relay (just the open frame relay component) from Grainger Supply, where I found an exact replacement - a 120VAC coil.
Then I wired in a standard wall switch in a little box next to the transfer switch housing, which picks generator voltage (when the generator is running) to turn on the transfer relay. So I have to manually switch the relay on and off for transfer. It's not important for turning on the transfer, but I like having manual control over the turning off proceedure before shutting down the generator. If I shut the generator down without having the shore line plugged in, the "whole house" inverter takes over and I like a clean transfer to that.
Hope that gives you something to think about.
Brian - K7ZRZ