The 30-338 is a great cartridge that has been around since the late 50's. My late uncle had an old Model 70 winchester 3006 that he rechambered in the late 50's to this caliber and it killed lots of animals. Since you already have a 338 win mag, you will have to rebarrel, so that leaves the choices wide open. I rebarreled my 338 win mag to a 300 ultra and used a new take off barrel. I only have 200.00 in this gun. My 338 shot great, but I didn't use it anymore since building my 338 ultra.
Remington model 700 300 RUM LH 26" rem ss/blued receiver lam stock 215 Berger @3025/180 NAB @3300
Remington model 700 338 RUM LH 27" Broughton 5C 225NAB@3300 /300gr Berger@2830
Savage LH 22-250