"I have a RIC First Pattern, and a .45 GAP round fits perfectly in the chamber(s)."
There is a significant difference in case diameter between a .44 Webley (.454) and a .45 GAP (.472). There's no way that a GAP round should fit in an RIC cylinder.
I'm wondering if your revolver was reamed at some point in the past for .455.
"Is there a shoulder in the chamber, or does it rely on the case rim for headspace?"
In original .44 Webley-chambered revolvers there shouldn't be a shoulder. If your gun was rebored, there may be a shoulder.
In any even, I'm guessing that the rim provides the headspacing on your gun.
I would suggest, though, having it looked over by a competent gunsmith.
Again, if a .45 GAP case fits in your cylinder, there's something odd going on.