The 444's 1:38" twist rate was set by Marlin, because that's what they were already using for their .44 Mag barrels.
The .44 Mag barrels using that twist rate? I have no definitive answer, but most people that dig into the subject tend to agree that it is a carry-over from .44-40. (And later also carried over to .45 Colt, because less tooling was needed if they kept the same twist rate.) A small group of people believe it is because S&W produced some of their .44 Russian revolvers with that twist rate, and Marlin copied it. But, as with anything Marlin, there's no paper trail to follow.
On the more obscure side, I've read that it goes back to a Russian specification for .44 Russian revolvers and a twist rate of 1 revolution per arshin (Russian 'yard'). However, it is unlikely that an official order would use a 38" standard for the arshin, when the more widely used arshin was 28". (More confusion and discussion could be had by looking at the various Russian 'inches'. But... I really don't think it's the origin of the 1:38" twist, anyway...)
But one bullet that is outstanding in the 444 from antelope does to bull moose is the 310 grain Lee gas-check.
If anyone here wants to try this, I recommend not going whole hog without testing first. Some 444s can't chamber the Lee 310 WFN without seating deeply (crimp groove inside case), due to the short throat (especially if sized 'large' or run unsized). And others can't be loaded into the magazine tube, because the wide meplat causes loaded cartridges to get stuck in a three-point bind with the loading gate (on the rim), receiver (on the case body), and magazine tube (nose of the bullet). (Clearancing the receiver and/or finger lever can fix that, but most people don't want to modify their rifle(s) just to be able to shoot one bullet.)
It is a very popular bullet with people that cast .44 caliber. So, obtaining samples shouldn't be very difficult.