I have a JP trigger in the first AR15 I built, but have since gone to the Giessele triggers (SSA-E & Hi Speed National match). So I have 3 AR builds under my belt and 2 MATEN MKM builds working. PARTS are the are the problem, not the part itself, it's the waiting for the parts that is getting old.
The parts list you list you have so far is heading in the right direction, Battle Arms safety is the way to go. I did have others but switched over all the rifles to battle Arms. The 3 AR15s that were completed and have the ones for the MATEN builds. I think I was able to score an Armalite AR10 BCG last night, the order does not say back ordered but I also don't have it in hand yet. So the barrel will need to be the AR10 platform. DPMS or Armalite both are fine to use.
I don't post as much, I read a lot here. I find the members are VERY good at helping each other.