Curious if you made progress here. If I read correctly, here was your status:
1. The battery is new, so you have full cold cranking amps 12.4V+
2. Your starter works, it engages if you take it off and have it bench tested (although, I have had one that passes at Autozone but won't turn a car over)
3. You jumpered over the starter while it's installed, so you know it will turn over the engine
4. You are not getting full charge at the relay?
5. You were not getting hot 12v on the main cable to the starter, so there must be an issue with that cable...or a connection there?
6. On the relay, I believe you can pull the relay out, and use a short jumper wire, and push it into the 30/87 diagonal slots and bypass everything, and the starter will turn over the engine.
I'm going through this with my son's 08 right now, with his we can push start it.
I didn't read anywhere that you tried to push start the Jeep, and if it works? We rolled, popped clutch and fired right up and ran fine. Can't start it, turn it and nothing, so I'm trying to walk the steps you are walking through.