There is an issue with your system. Go see another dealer, this usually ends up being a software issue and they re-flash the amplifier. Very common on the vehicles with the HK stereo systems.
As a former professional MECP certified installer for 15+ years here is some advice: Run, run, and hide from the Linkswell. It looks like garbage, performs like shit and does not retain all factory information. I would bet $1000 you will not be happy with it. Go with the Stinger Heigh10 or the Alpine ReStyle both of these look OEM.... if you must change out the headunit. I personally wouldn't and use the CH41 mentioned above.The only benefit to going aftermarket is a larger screen. The CH41 will give you perfect and simple amplifier integration.(It is also plug and play)
Subwoofer - stick with one and go with it. Otherwise you have two subs in different enclosures. It is a recipe for failure and disappointment. You mentioned a stealthbox but posted something that looks like I made in my garage when I was 16. That BRP box is hideous. This is the real stealthbox:
SB-J-JL4DPAS/10TW1-4
The rear speakers brackets look really good - but not sure if they are needed. I haven't even looked at the 4xE alpine system - but most of the Jeeps already have 6.5s so this may not be needed.
Everything you posted will sound like dogshit compared to working Alpine factory system. If they are re-wiring the speakers than that means they are by-passing the amp. That means your factory tweeters and 6.5s are tied together with a cheap bass blocker running 15 watts of the Linkswell, rear speakers are getting the same power. Not sure where power for sub is even coming from.
If a shop recommended all this - run and hide from them. Sounds like a ghetto backyard shop to me, probably will end up being messed up and broken panels. You have a $60,000 vehicle - don't cheap out on this project.