I'd go 7 PRC for your stated purposes. I am gathering parts for a rig similar to what you describe right now. It will be a Tikka action, 22" threaded, light contour barrel, Stocky's VG, Bushy 3-12 LRTSi. I've hunted with a very similar 7mm RM for years, so not really breaking new ground, but the 7 PRC is a much better fit for a Tikka.
The BC is intetesting, but I have read reports of heavy bolt lifts and other overpressure signs with them, so not sure its the best idea with extant actions? Time will tell on that. Further, I don't need more performance than I can get from a 7 PRC; honestly, I don't even "need" that much. An 18" 6.5 CM or 7mm-08 can accomplish about anything I need out of a big game riffle, and I should be building more lightweight, handy, short action rigs instead of more long range magnums, but a guy likes what he likes.
I have a 1:8 300 win mag with a long throat that I assembled just prior to the 300 PRC coming out. It cuts tiny groups and is exceptional for delivering a largish hunk of lead to far off targets; however, with heavy bullets over 76 grn H1000, recoil can be onerous. I don't run it with a can because recoil reduction wasnt enough, so went back to a brake with ear muffs. The rig weighs 10 + lbs with scope and ammo. More with a bipod. I generally prefer a lighter rig for elk country, and I dont care to go lighter on something like a 300 PRC.
As far as the 6 UM - I'm sure I'll get push back here, but I'd go 6.5 PRC all day over a proprietary round that, based on what I read on these foruns, has had some developmental hiccups. I'm sure the recoil threshold for routinely spotting shots vs not is different for each person, and that, by extension, the breakover point for a few folks could fall between a 6.5 PRC and a 6 UM; however, it seems more logical to me that any reported difference in recoil and shot spotting between a 6.5 PRC and a 6 UM shooting similar BC bullets will be more attributional than actual. Further, any quantifiable difference between the two is likely to be so minimal that its not likely to be paradigm shifting.