Thank you again, Rami Tamimi! Well, we're leaning towards taking the 8am flight to avoid any risk of IST weather delays, so that means the airport hotel. I was able to find documentation that Jordan Pass only waives one entry visa. So the idea would be to arrive, get a transit visa, then on return to AMM show the Jordan Pass to get the tourist visa fee waived.
Arriving on TK, transiting to RJ, less than 12 hours total, American passports, will the transit visa be free (and if so, head to normal immigration or to the RJ transit desk?) -- I can't seem to find the cost vs a single entry tourist visa?