Ok, I've established with Pacific Tool that this reamer isn't proprietary, they sent me a print of the reamer, and can make it at request.

However, I don't see dies under this exact name.

I see 375 Hawk and 375 Scovill...

I'm inclined to believe that the 375 Scovill is the correct die, and the Hawk/Scovill name was just giving credit to the original design.

Can anybody verify this?

FYI - the Pacific chamber print shows a 17 degree 15 minute shoulder, at .454 diameter, with a .404 neck diameter, and .470 base. (Whelen brass? - my initial thought is the neck sounds thick???)

The thing of real importance here is that the dies match the chamber. What you're talking about is basically another 375 Whelen Imp, as created by Scovill. The guys at Z-hat, recognizing the potential, jumped on it and made it part of their "Hawk" line. Just make sure whoever does your dies has a few fired cases from your actual chamber and you're good. You should be able to get the die maker to tell you the specs of their "Hawk/Scovill" die, and you can compare that with your reamer.
If it were me, I'd use have a reamer made for the little-known 38 Taylor. It has a .4550" shoulder at 2.1585, and a 30* shoulder. Almost 75g water capacity.

Isn't one based on the '06 and the other on the different but similar 93. x 62? I know there is a usable difference in case volume between the two.

Check out Z-Hat's site. They explain a bit about it, and why it has different names.

The 375 Hawk cartridge was originally designed by Bob Fulton, of Hawk bullets and Hawk cartridges association. It was based on the 9.3 x 62 mm. Bob showed the design to Dave Scovill, who modified the design to use the .30-06 base case instead and christened it the 375 Scovill. The difference is about 0.001 or 0.002, depending on the brass source. As currently cut by Fred Zeglin (Z-Hat Custom) and loaded by Quality Cartridge it uses the .30-06 brass and they call it the 375 Hawk. That is how mine is set up.

That is correct, the Hawk used 9.3x62 brass, the Scovill was designed to use .30-06 brass, as it was obviously more available. Loading data will be the same which is why you see it listed as Hawk/Scovill.

"as created by Scovill" This cartridge was not created by scovill and '06 brass was used by Bob to load the original 375 Hawk that Bob created. The 375 Scovill is what you want to build as listed in the Barnes manual. '06 brass (no belt) and 59 grains of powder will push a 250 grain bullet to 2700 fps as Scovill found out and had to have. Same power as a 338 mag with a larger bullet and less recoil. My daughter shoots mine very well.