Sometimes there can be an overwhelming amount of "Jeep jargon" when new to the Jeep world. (SYE, CV, transfer case, etc)
A simpler start to see if you have a SYE is to see if you have a double cardan joint on your driveshaft. (not a guarantee, but a likely indicator).
That means look underneath the Jeep and count the number of "u-joints" on both sides of the drive shaft.
U-joints being the "X" or "+" shaped things that look like ninja stars with round ends.
If you have 2 u-joints on 1 end (and most likely 1, but possibly 2 on the other end) - you most likely have a SYE; or at least have a double cardan joint, which means you probably can raise the skid plate up.
I say "probably", because there may be other issues, like the pinion angle at your axle...which may need to be modified with the control arms.
If you only have 1 u-joint on each end of the driveshaft - then the best solution is to install a SYE kit and CV driveshaft.
(I have no other recommendations actually. A motor mount lift might help it a bit. I had a SYE/CV installed last year and wished I could have afforded it earlier).
Please note that you *MAY* require adjustable control arms for your rear axle when doing the SYE. (You are right - it's not a cheap or simple upgrade.)
Edit: forgot to mention - another option is to take a picture of the driveshaft and post it here. (Also note - my transfer case has a tag on it facing the rear of the Jeep that states what model it is).