Having both the 405 and the 444.
Hornadys factory load for the 405 wcf is 2200 fps with a 300 gr bullet.
If handloaded, 2400 fps is reachable within safe pressure limits.
It's easy to duplicate the factory 405 load with the 444.
Just take Speer #13 manual.
55.5 grs Hodgdon H335 behind Speer 300 gr Uni-Cor for 2211 fps.
But 2400 fps with a 300 gr bullet in the 444 Marlin within safe pressure limits, it's absolutly impossible.
But, for longer range, take a look at Vihtavuori powders.
They list Hornadys 265 grs bullet to over 2400 fps with VV N120 and VV N130.
And that is out of a 22 in barrel, within safe pressure limit.
Run that load trough a ballistic calculator and look at the trajectory.