338 AM is big but I want to stay with the 338 T or 338 lapua imp and I'm leaning towards the 338 T
My 338 AX is exactly what your looking for. Its a very modern version of the 338 Lapua improved. Designed it back in 2007, released to public in 2008. Hundreds of them out there. When i designed it, Shawn Carlock had his 338 Edge running hard. Great round. That would get you 2800-2850 fps in a 30" barrel.
designed my 338 AX with the same case body taper and shoulder angle as all my other 338 lapua based wildcats. Case body taper is slightly more then a conventional AI case design but this is a requirement to get great extraction performance at top working pressures. Something the standard AI design on the lapua sized cases can have issues with.
as such performance is significantly improved. My case shoulder angle is also slightly less aggressive at 38*. Perfect for controlling case stretching and everything else the shoulder needs to do but feeds noticably better then a full 40* shoulder angle.
in 26" barrels we see +2900 fps all the time with a 300 gr berger. many will comfortably do 2950 fps in that length barrel. And thats with a relatively short 3.670" oal to fit in any mag designed for the lapua diameter cases.
in a 28" barrel its normal to break 3000 fps. 30" barrels even more. All this and still using a conventional long life throat design, no magic throats here the WILL reduce throat life to some degree. Just plain old, old fashioned good long life design.
after years of Shawn trying to make his EDGE run with my AX with special throat designs and such, it still needed a 30" barrel to match what my AX would do in a 26-27" barrel. As such, the 338 Terminator showed up to match my 338 AX!!!
the 338 AX would be a perfect option for what your goals with this rifle! As would be the Term. They are for all intent and purpose, identical in nearly every way.