Peter Kilduff's new book,
may address the subject of MvR/Reinhard's successors--Manfred specified Reinhard as the next CO and evidently there was no objection from higher authority. But neither Udet nor (especially) Loewenhardt had the requisite seniority when MvR died--he and Reinhard both were captains. Of the 9 JG kommodores, 5 were captains and 4 were oberleutnants. I don't know when U & L became "obers" and therefore potential rivals for Goering's slot but suspect they were promoted sometime after he arrived in July.
As for the presumed feud, I'm unaware of any documentation. Obviously ComJG-I was THE prestige assignment in the GAF but I suspect any healthy young Teuton would have been delighted just to be a member, let alone a squadron commander (Udet took a "demotion" from CO J.37 to join JG-I) with lots of targets in easy reach.