Take a closer look at 6.8 Western. All the advantages of modern BC Numbers on a 270 bore, but not as much recoil as the 7s and 30 cal. For those that know, they love em.
Not sure what the rules are... If modern cartridges are allowed or we're supposed to pick an older chambering... So I'm throwing out one of each.
Older - 7 Rem Mag
Modern - 7mm-6.5 PRC
I've found the same thing with 7 rem mag... Hornady only loads up to 162 gr, but has data for 190-200 gr bullets. Only thing I can think is they don't want to produce any that completes with the 7 PRC.
I would add where are they comfortable placing that shot? If they're just going to shoot double lung, that's nearly a 2 MOA size target at 500Y... So a 1 MOA gun/load would be more than sufficient.