By weird or odd ball, I understand that to mean you want to be able to buy loaded ammo not have to hand load.
Using that:
300 Ultra. This chambering is quite capable of taking game at 1000 if you find factory loads it really likes. If you want to hand load, I'm sure you can find a load that will put over 1000flb of energy on target at 1 mile.
7MM. While lots if the guys recomment the STW, there are 65 different factory loads available for 7mmRM at Midway including a long range target load. That said, if it were me I'd go 7 Ultra or 7 WSM. Just me. Actually I have a couple .284 Wins and one of those will become a 7mm/26 Nosler.