Follow-up
Just to follow up based on my experience: RJ did in fact check my bags through in BEY to LHR via AMM. They even issued boarding passes for the connecting flight the next morning on BA, which was good because ba.com and the app didn't let me check in online (I assume because of the mixed airline ticket) and I knew the LHR flight was very busy.
The Amman airport hotel desk, for anyone repeating this journey, is accessed airside at the interntaional transit area. The guy at the desk gave us vouchers to waive the requirement for the visa and then his colleague escorted us through immigration and to the bus.
The next morning we were also escorted off the bus through security and immigration to the airside area. The whole thing went quite smoothly. The hotel itself was fine for a night; had we had more than 7 hours I would have preferred to stay in downtown Amman, but even as it was we didn't really get enough sleep.
The ridiculous UK laptop ban meant a very thorough search for electronics at the gate, but we had checked in our laptop and iPads at BEY. One of our bags (the one with my laptop, naturally) didn't make it on the BA flight, but it did arrive on the same flight the next morning, intact.
The upside is that we received opups from Y to J.