Hey everyone - thanks for the suggestions.   

I've been slugging with pure lead. I don't blame some of you for asking to confirm the measurements. I pulled out my second (less trusted) micrometer and got almost the same readings.  BUT in the interest of scientific rigorosity, I've got some cerrosafe around and I'll pour it down the muzzle and see what it measures, just to be sure.

However, I also tapped one of my slugs into the muzzle to see what would happen. It's a Bufffalo arms 378365 E2, I measure it at pretty much at the .38-55 spec of .3775".  When I tap it into the muzzle, I get a shoulder of lead gathered at the rear, and more importantly, the barrel lands wash out the grease grooves, so I get a solid band of lead for each land.  I'll post pictures when I can.

So again I will cerrosafe the barrel, but at this point
Either GM messed up, or Buffalo Arms AND my two micrometer manufacturers messed up.

But like I said, it's already on the gun and finished (rather nicely) so I'm inclined to order a custom mould and see if I can make that work.

One other data point - there are no markings on the barrel. I trusted the gunsmith to put a GM on it.

-Nick

Nick,
If you are getting dimensions to repeat I'd trust in that.  Give it a whirl and have a mold made to fit.  I've been involved in a couple of these fiasco's - they're are a bastard child but some turn in to very pleasant surprises.   The shallow grooves aren't really a concern but you may want to experiment with your alloys, even consider trying paper patching.   
Another concern you have with an under size bullet such as this is the case itself, are you shooting black or smokeless?  breech seating (the case doesn't matter then) or fixed? make a cast of the chamber and pay close attention to your case length - stay within a few thousandths of length.  If you're using smokeless and fixed ammo I'd suggest sizing the first 1/4" or less of the "neck" or mouth with just enough to hold the bullet, if black, forgo any thought to resizing, use a cork card and grease cookie under the bullet... 
You slugged the bore was that just at the muzzle?  Can you push a slug the full length of the bore and see if there is any uniformity from end to end, tight spots and loose spots?   Loose at the muzzle - tight at the chamber end will rarely produce anything appreciated.
I'm rambling but I've tried a few of these and made a situation like yours - shoot remarkably well.
Greg

Dragging a long handled cotton swab in and out of chamber/lead area and muzzle area will often pull strings of cotton that you can see with a bore light too if there are burrs.

Ok so here's a picture of one of the Buffalo slugs (.3775") tapped into the barrel.  You can see (arrow) where the slug has a new shoulder where the lead has built up from the second to last grease band.  Also the larger size of the final band. Also the stripe where one land washed out the grease grooves.  I'm thinking that barrel is too small.

Haven't cast the chamber or pushed a slug completely through it yet. I'll do that before ordering a custom mould.  If it needs to be so small that the case won't hold it, then I'm getting a new barrel.

I don't mind paying for quality, but I thought GM WAS quality.  I bought a drop-in barrel for my Hawken that just drove tacks.  Guess anyone can make a mistake.

Just updated again. The first pix was way too big.