Welcome to the wonderful and confusing world of .38-55
Having a couple of rifles in this caliber I've run the gamut of bore size and brass length variations.
First off Starline does indeed make both lengths of brass. And without trying the cases or casting the chamber it's hard to say what any particular gun is chambered for. But from the reading around it appears that many of the older single shot rifles used the longer 2.125 while the later lever rifles went over to the shorter 2.08. Given the birth date of your Marlin the odds are good that it's set up for the 2.08 length. But it would be worth chamber casting to be sure. Or just shoot the 2.08 stuff and live with the slight gap. It's sort of the same as shooting .38Spl from a .357Mag gun. The fit and shoot just fine. But there may be a crud ring formed in the chamber over time due to the shorter casing.
And the .375Win brass is indeed another roughly tenth of an inch or so shorter than the 2.08 38-55 brass. So it will chamber just fine. And in a 2.08 chamber it does mean that you may need to adjust the bullet seating depth to ensure it fits the elevator and feeds in neatly. So longer and heavier bullets may be required if your Marlin proves to be sensitive to OAL during cycling and you still want to use .375 brass.
I've got the worst of both worlds on one barrel. The chamber is sized to take the shorter 2.08 casings and set up for .379 size bullets. But the bore wants the older and smaller .376 bullet size. So in playing around to find what works best I bought some .375Win brass so I'd have thicker walls to better center and seal the small bullets. The plan to work with the shorter yet brass is to try some home cast 300gn bullets that are longer so I can seat the bullet in the neck fairly well and still have the ogive resting against the leade. The key for your Marlin here is that .375Win casings do add another variable to be aware of.
In your case I would still suggest you slug the bore. This is pretty easy. You put a soft lead round ball on the muzzle then pound it into the bore with a plastic or wood mallet then punch the slug down with a close fitting wood or brass dowel or some such thing. Then a cleaning rod will push it down and into the chamber where you can retrieve it for measuring.
The old gun crowd has a lot of folks that enjoy using smokeless as well as the ones that shoot BP. There's a wide variety of low pressure smokeless loads that will do just fine and be safe in that Marlin provided there isn't any pre-existing damage. My own favourite is an 18gn load of 4227 behind a 255gn cast bullet. I've shot these with no packing but recently I loaded up some with a printer paper over powder card with a small tuft of polyester pillow stuffing to hold it in place. I've yet to shoot the loose and packed loads together for accuracy comparison. I do know that when I drop in that 18gns of powder it looks like a LOOOONG way down to the charge. So the idea of the paper separator and tufting is to hold the powder consistently back by the flash hole for a more consistent burn.
These loads push the cast bullets I'm using along at around 1300 fps. So shooting out past 150 yards or so becomes a largely "rainbow" like affair. With jacketed bullets and once the barrel and chamber is proven to be sound you should be able to up that to around 1700 to maybe 1800. But watch your peak pressures in this old girl. It's not a modern Marlin Guide Gun that'll accept over powered 45-70's. And I would sure not want to shoot any modern .375Win from it. Not even on a dare.
That's a very nice looking old classic. Hopefully you get it running well. My own feelings are that this is old enough and in good enough shape that I'd be highly reluctant to re-blue it. I'd probably just use the oil and steel wool trick to smoothen up and blend in the rust spots I see and call it a day. If the goal is to hunt with it I'd also use some nautical spar varnish to fill in any cracks in the present finish. I'd likely also apply boiled linseed to the end grain in the action inletting areas of both the fore and shoulder stock and under the recoil plate. Again to aid in weather resistance for the old girl.
