While not concerning an actual single shot, don t kick me off the island, I do have several S/S in the safe.
   Its a cast bullet issue, and where better than to ask here?
I have both an original 1893 Marlin, and a modern 336 Marlin "cowboy" with the Ballard rifling in 38-55.
    I was aware that the old Marlin 3855 had large bores but was surprised to learn the modern version does too. Both slug .381
    Standard bullet sizer are .376. Both guns shoot a good improved cylinder group, (with cast) pretty much no matter what. Well maybe a modified on a good day.
    I annealed a .376 die, and polished it out to looks about right and get bullets .379  Now Murphy appears, and the modern marlin chamber neck is so tight, it won't accept the seated bullets. The vintage gun, does chamber, but tighter than the proverbial bulls butt.
    A couple options seem possible. buy another die, polish it not so much, it would then chamber but still rattle down the bore.
     I would be tempted to pull the cowboy barrel and polish the neck area a bit, till it accepts the larger bullets, but that would be risky at best.
   Shoot way soft bullets, but then they might lead like a bad boy.
   I know that one mold maker,  can't think of the name right now, who makes one heck of a good mold, offers to bore them, to match the lead mix. 
    I have yet to contact him. In theory, they drop from the mold, correct size, and just hand lube them. I am not a serious competitor, nor shoot these guns that much. I am just picky
Open to ideas and suggestions, thanks! I always was mystified why Marlin ran their 38 55 bores so much larger than Win.
Ron

I ran into this with an old Marlin in 38-55. My question would have been why did Marlin stick with undersized chamber necks once black powder was no longer in general use to bump up the undersized bullets? I sold the rifle. My Uberti has a .379 groove but will chamber .380 bullets.

Use black powder!

I had a similar problem with an H&R rifle in 38-55.  I slugged the bore and the rifling required 0.380 bullets but the chamber was cut for 376.  I had the gun re-chamber to accept the .380 bullets.  It now shoot great.

This is a pretty common problem with many .38-55 chambered rifles, and I'm not sure why? But the fix isn't to alter the chamber, or thin case necks. Once thinned enough to allow chambering a .381"-.382" bullet, the cases wont make it past cleaning, as the necks are so thin they come out of the tumblers dented and almost ruined.
The fix is to have a mold maker like Accurate, or any custom maker, build you a mold that's basically a heeled bullet design. Make the first two bands (or whatever depth you need) small enough to not bulge the case. Then the remaining bands at the size you need to seal the bore. 
I've had several friends who had Tom at Accurate build molds this way and love shooting their guns in .38-55 with larger bores now. I've also seen a fair number of chambers ruined and later sold to unknowing buyers by owners who thought they'd "improve" the guns by opening up the chambers. In a couple cases friends had to rebarrel or reline barrels when they discovered some idiot ruined their chamber.

On the Starline web sight there is a good explanation and cure for the problem you are having.  Good reading. Starline brass may solve your problem.
 
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JLouis wrote on Apr 8^th, 2021 at 1:03pm:

 
They offer thinner necks and also two lengths 2.080" and 2.125" depending on 
which you prefer.

I think I would have Mike Lewis fix the chamber.  I would have zero fear (McPherson) of not being able to address it.   McPherson's writings specific to the chamber reaming are not reasonable.