LP powered microwave... Well, basically not possible, (Though you can power a generator with LP and power the Microwave witht he genny)
There are, however, infrared ovens that cook very swiftly, but they are NOT Microwaves. totally different means of cooking.
Your RV microwave is a basic home counter top type. it may have a few minor mods (External to the case) to duct exhaust air to the place the manufacturer wishes it to go, in my case out the front into the kitchen, in other cases out the wall to the outdoors. You may need to make a special air duct for it, Nothing major.