The Swift A frame seems to be the go to Bullet for many of the hunters that have taken much game. I am sure it would work for you. I would also suggest trying the 300 grain Hornady XTP in your 444. It will give you close the velocity of the 240 bullets with better downrange energy.
"Therefore go and make disciples of all nations,... "
Handgun hunter since 1979 - haven't used a rifle since!
HHI member #992, NRA, SCI.