Sometimes it helps to get wider perspectives.
In my opinion everything from a 270/7mm through the 300's (308Win, 300WM, etc), 338WM, 35 Whelen, 9.3x62 are good, all around, medium caliber hunting rounds. The 375Ruger and 375H&H are in a marginal zone. Magnums start with the 416's. Recoil can be re-assuring. But since this is the Long Range Forum I do see extra value in sending a particular caliber's bullets a little faster than for normal hunting. People like to call them magnums but the same bullets do the work. The 30-06, 300WM, and 300PRC all send out the same bullets.
Anyway, if caliber size is new, you might try shooting some 375's and 458's. Then the difference between a 7mm and a 300 will not relate to bigness and you can concentrate on whichever rifle and bullets you want to hunt with.
I understand your perspective. I think many would call the calibers you referenced super magnums. Things that require on oversized bolt, action, BF, uncommon parts, etc.
Given the standard action cartridges 308, 06, 6.5 CM, 270, etc - most people accept magnums to be 300 wm, 7mm, 300 PRC, 338 wm - with the upper end being 338 Lapua/edge.
Jumping into the cheytac, bmg, and dangerous game rifles is a different arena. The first 2 are discussed often in the ELR forum and not nearly as often in the long range forum. Also note this group of guns is often far heavier and less practical than most hunting rifles.
You could make a feasible argument that magnums start with 70grs of powder. But that's a another discussion.
Since the OP is talking elk, Broz has noted in many forums that the 7mm has not been as effective as the 300, despite what the paper ballistics suggests. He is well respected and can't explain 'why' there is a noticeable difference. I don't have anywhere near the experience he does with elk. I can only discuss my experience with a 300 wm + 215 Berger loaded @2875 fps does to elk (leaves them very dead).
Although I've only been hunting 30 years, I've never seen "too dead".
Feel free to PM me if you'd like to discuss this more. I don't wish to side track this thread.