Recently there was a thread about dimensional differences between various makers of reloading dies.
I have a Uberti HW in 38-55 (Ballard length) that has a 0.383" grove diameter. I had a mold made to correctly fit the bore and a friend made me an expanding plug to open up the sized cases so the bullets will seat properly.
My issue is I'm sizing the cases with RCBS dies and they are for bullets in the 0.376" to 0.379" range.  This works, however, I think it's over working the brass and the bulge from the bullet is very apparent.  Does anyone know of a sizing die made for a larger bullet?  I assume Uberti made their chamber and bore more like the original barrels and not the common 0.375" ones found today.

The modern size dies, can be a problem for the .380 groove.

They way they make them, is to size down, at least .005 below chamber size and then the expansion button, pulls the id of the neck up to about .002-3 below jacketed bullet size. So, in your case, the button will be about ~.373 and the die will be sizing the id to ~.370.

A suggestion is, if you can find a 375 Win die set, try it w/o the sizing button and see what you get. The 375 Win, has thicker brass and it may get you a little larger neck by ~.003.

And you'll need a button that's you bullet size or .001 under that. Remember the brass springs back about .001.

You can also use a "M" die and expand the necks, you won't get the bulge using it but, your still working the brass.

Frank

I size my 38/55 Brass with a interchangable neck bushng die from CH4D. After sizing run the case in a Lyman M die that’s a slip fit, does not change the neck size at all, gives a very small flare to the neck that facilitates thumb starting the cast bullet. 

Seating the bullet adjust the seater to push the flare out. I can chamber without ironing out the flare but guns chamber is doing it anyway, might as well de - flare with some control .

You would think measuring the bullets Diamater, case wall thickness, then how much bullet pull you want you could calculate what neck size die to use. My experience is you can get close but some trial and error needed to come up with the correct neck bushing. Not enough pull your thumb can push a seated bullet down in the  case. No need for too much pull best get it just right. 

Using this  method and a 500 case lot of WW Brass since 1994. Sized 140 down to 32/40. 360 remaining 38/55 cases, less about a dozen lost one reason or another, are in good condition serving well. Have anealed and trimmed twice.  Be hard to figure exact firing per case count but it’s a lot.

Factory F/L set, no consideration my bullet chamber or bore size result would not have been as good. 

Could look at notes and give you exact bushing sizes, but my bore is .375 data not relivant to your outfit
P

Boats 

You can get an adjustable barrel lap for about $10. Use it with a lapping compound to lap out a sizing die.

Here is how to lap your die.

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I do what Randy mentioned for my .38-55 loading. I either raise the dies to not fully size, or at least enough to only size them to fit the chamber, and bullet diameter. 
I also use the M die that Frank mentioned, but couldn't find the size I wanted, as Lyman's choices are not great. I bought a larger .40 caliber plug and turned it down to the .383" size I needed for my .38-55 Lyman sells the plugs very reasonably, and I often buy larger plugs to turn down. So I've got a few dozen plugs in a wood block, and just use two M die bodies in long and short lengths.

I have a pair of M die bodies in long and short that I bought used at a gun show many years ago. Someone milled the sides of the threaded body open so you can see the plug enter the case as you raise the ram. A very neat feature, and it makes it easier to open necks, or bell case mouths when you can view the plug. Too bad Lyman doesn't do this on all their M dies.