The transfer switch to our fridge just got replaced. It went out. I found one on e-bay for $75.00 and received it in 3 days. I asked the dealer and they wanted around $125.00 for it, but did not have one on hand either.
Try to get a voltage reading from your inverter and the transfer switch. If your transfer is the black one with the special connectors it takes less than 5 minutes to change out. I had 2 mounting screws for the switch and 3 more to hold the wire loom in place. If you can post a pic of the switch.
Just for fun I went ahead and priced an inverter from the dealer, $750.00.
Here is a pic of the model we have in our Road Warrior:
[FONT=Verdana,Arial,Tahoma,Calibri,Geneva,sans-serif]https://www.ebay.com/itm/MAGNUM-CSW-TS15-TRANSFER-SWITCH-15-AMP-FREE-SHIPPING/254172822880?hash=item3b2de17d60:g:yHQAAOSwCR9clC34:sc:USPSPriority!45373!US!-1[/FONT]