When I was considering a gun/cartridge for ELR, I too wanted to stay 30 caliber or under for a different reason. I landed on 300 Norma Magnum.
Assuming by 338 you mean 338 Lapua, the 300 Norma Magnum, 338 Norma Magnum and 338 Lapua Magnum all share the same bolt face. That makes...