I'm contemplating building a .458 SOCOM on a bolt action rifle, which I would handload both sub and supersonic loads for.

The .458HAM'R seems to be more of a reinforced case with a thicker web and small rifle primer, than an improved chambering.

Would it work to size HAM'R brass in a SOCOM die to shoot it in a SOCOM chamber, (in a bolt action remember) to gain the added speed the round offers with the 300 and 265 grain bullets?

You can use SOCOM dies to reload HAM'R cases, just backing it out enough to get the correct headspace.

The .458 HAM'R seems to be the same case with the shoulder moved forward ever so slightly, presumably more to prevent it from chambering in SOCOM chambers than for performance, but I can't find the case dimensions for the HAM'R so I don't know what the difference are.
Supposedly, you can't tell the difference by looking at them.

With those extra 200fps the 300 and 265 grain bullets the HAM'R brass brings the SOCOM into another territory, 2400fps might become possible with the 265 or 250 grain bullets.

The pressure of the 458SOCOM is limited to 37,500psi with it's use of pistol primers in the AR-15 platform.

The Ham'r case uses small rifle primers to 46,00psi pressure to be run thru the AR-10 platform.

In this day & age-
Look at the bling of the 6 & 6.5 Creedmoor-
Basically an improved 22-250 case blown out to remove taper & shoulder moved forward to gain powder capacity.
22-250 & Creed cases weigh the same
case head/webs are identical
one runs at 50K
one runs at 60+k

I thought we answered this same question here in another thread.
The socoom case is NOT limited in pressure. The Hamr case is NOT made to operate at a higher pressure. It is the rifle platforms upon which they are built that are the limiting factors
You can put a socom on a bolt action and shoot it to 60K psi, all day, with socom brass. Do not think the rebated case is weak; not sure where that idea came from.
Do you think the 284 Win case is weak?
Additionally, the rebated case is exactly the same head as a 30-06; .473 head with LR primer. Weak?

Now, if you want a bolt action .45 caliber cartridge, the 450 Marlin or the 458 American/ two inch is a better option. I have built many of them on Mausers.