The best advice for a 38-55 in a Model 44 is: Do Not shoot it.
The Stevens 44 is not an action to use for a cartridge that powerful.

Just some observations. I've got two of the larger calibre Stevens 44s. One in .32/40 and the other in .38/55. Both have the "safety lug" on the hammer. The bore in the .38 was complete shot and the action was very very loose - there is a message there. So I had it relined to .25/21, replaced the link and main thru pins (breech block & lever) and breech block. It is still performing well with light smokeless loads with SR 4759.
The .32/40 was in great shape with a spotless bore. It hasn't loosened up at all after 10 yrs of light use, though I have only ever used it with BP or duplex loads and a 165 gr slug. (A question for Pete here, when you had to replace the link in your .32/40, were you using BP or smokeless loads?)
I'd play it safe with that .38/55.
Spud

Spud,

  The first links and pins I replaced were because the gun was loose when I got it. The 2nd set on that one, and the set on the other I've done were all shot with smokeless powder. Can't recall now whether either had the "safety lug" on them. Would have to look it up to give you the loads and MV's, if I still have them. Got rid of the guns probably 15 yrs. ago or better. None would have exceeded 1400 fps tho and were shot with 4227. Bullets ranged from 165 to 180 grs. Never used BP or duplex loads in them.

  One other thought on this that I just remembered. When you replace the link and pins you have to decide whether you want to harden the pins. I didn't which might have contributed to early failure. If so, and the hole enlarges on the lever and breech block you could be faced with replacing them, along with the link again if you didn't harden that. There's not a lot of room around the hole in the breech block and reaming them out if they elongate might make them weak enuf to fail, which would drive the case back into your face.

PETE

Spud would you care to share some loading info on you 25-21, have one in the works?  Use 16.5 grs. of 4759 in my 38-55 with a breach seated pope style bullet.  This is in a Stevens 44 1/2, Not a Stevens 44.

Hi 38-55.
My target load for the .25/21 (13 inch twist) using 95 gr lyman 25720 cast 20:1, 8 gr SR 4759 with cotton wool filler, Win SR primer. This load shoots better with a harder lube - Alox & beeswax 50:50, than a soft one. These are fixed rounds. About to start some breech seating using a new base band slug (Dave Farmer mould). I tried SP primers but the SR performed better.
Using Bertram cases with no major problems so far. Far easier for us here in Australia to use a local product. You would not believe the hassles we have in importing gear from overseas. That said I've got some cases coming from RMC soon and am keen to see how they go. Will use them for breech seating. Good luck with your .25/21. It's a great little cartridge (for rabbits as well).
Spud