Hi Sheepdog. I don't know about rental companies but I did have a propane oven in my popup that I traded in this year.
Propane ovens are really of limited use. Mine operated with a pilot light way in the back of the oven. To light it I had to get down on my knees and reach one arm with a lighter back to the pilot while raising the other arm up over my head to keep the knob pushed in for the gas to flow. It was a little like playing Twister.
I know your rental company could set the pilot light for you but if it went out it's awkward for someone unfamiliar with it to try to get it relit. Also as far as ovens go, it was small inside (couldn't handle a 9x13 cookie sheet) and while it had a temperature knob with 250-300-350 etc., it was accurate to +/- 50 degrees and wouldn't get very hot at that.
I've always looked over the years at popups and trailers and I've seen that oven (same brand and type) in units up to the present day. It doesn't go in high-end units so I can't say any unit you would rent would have it, but I honestly think if you did use it you would be unsatisfied. It doesn't cook like your oven at home.
We had a thread on ovens and Greenberg about a year ago (use our search tool - I found it). The rental trailers are a great alternative for folks who want to camp at the Fort but don't have the trailer to haul there (or it's too far). Having an oven sounds like a nice option but in reality it doesn't add very much at all net-net.
Hope you end up having a good experience with a rental unit.
Bama Ed