This seems to be a common problem with that particular Sharp model that was used in RVs years ago. However, as you can probably guess, it's more expensive to fix it than to replace it. I think I remember that the control board or one of the circuit boards has to be replaced.
I do have in my notes that several replaced the R-312AK with several Farberware models.
One that's currently available is the Farberware FMO11AHTBSJ
Here it is at Home Depot:
Black 1.1 Cu. Ft. Countertop Microwave in Black Stainless Steel with Smart Sensor and Inverter Technology
Of course, I'm not certain what faceplate measurements these other RVers were using as I don't believe it was a "Gulf motorhome" but they did say that they had to drill additional holes in the oven in order for it to attach to the existing mounting provisions.
The cutout dimensions for the FMO11AHTBSJ are:
20" width left to right
17" depth front to back
Measure your faceplate again to see if it will fit. If not, I suppose there's always the possibility to have someone make a custom faceplate for you.