from your post above - your selector assy is faulty.
What does it do? or not do?
The reason I ask is that I have just replaced my gear selector - and my mate has done his too!
My symptoms were - the Jeep would go into gear when first started then even 5min later would not select any drive!
My mate had repeated limp home mode issues them it eventually went into permanent limp home with a code of P0702.
Both cars showed the same at the shifter - switch the ignbition on and check out your gear select mimic lights - No Lights! put the select into R and check the reversing lamps - No lamps illuminated!!
Both cars were fixed by fitting a new selector assy - think £765 ish
According to the Jeep mechanic - these units failed regularly through the years. and to answer your question - yes you can fit another gear selector unit the Quadra Trac or Quadra Drive applies to the LSD fitted to the diff and nothing to do with the selector
If you do not have any codes up or Limp home mode, you can swap over the selectors, as there is no need to pair it up with the TCM.
My mate's P0702 code had to be reset by a Jeep DRB machine.
Good Luck