Hi, Paul!
I am disadvantaged in not having a Stevens 44 in front of me at the moment, and it's been several years since I examined one.
From the Frank De Haas "Single Shot Rifles and Actions" book, it is stated that the back of the breech block bears against shoulders in the cast steel receiver when the breech block is propped up and closed by the lever and linkage. He did state that any looseness in the various pins for linkage, lever, and block are accumulative and results in excessive headspace. He listed the five stress areas mentioned earlier. From his description, some of the 44 improvements included a lever tension screw that is adjusted to keep the lever in the up position.
He did mention that this is one of the weaker single shot actions, and he advised chambering/barreling only for .22 rimfire, .32-20, .38 Special, or keeping the original .32-40 or .38-55 target level loads in the 20,000 psi catagory. I would restrict it to black powder loads or very light smokeless loads ONLY. He did not mention .45 Colt, and I suspect it was because he considered the total breech thrust to be excessive, even though it is a moderate pistol caliber pressure, but with a larger cross-sectional area, and therefore the back thump would be much more than say, .38 Special.
My educated guess is that for your purposes, the 4140 HT is plenty strong for all the pins. Probably even unheat-treated drill rod would work okay for those calibers. I would definitely not consider chambering in a magnum pistol caliber or anything more muscular than that mid-range 170 grain cast bullet at 1550 fps.
Sounds like an exciting project. Show us some pictures and range report when you finish!
John