Hrm. Thanks for all of the replies, guys.

I figured there'd be some nice suggestions from the peanut gallery.
We had a talk about it at the table again today and I laid it out that I didn't much like the second character concept and that retiring a PC for one over-powered ability getting nerfed was below him. Which, honestly, we all agreed with, even him.
Eventually we reached a comprimise. I downsized the penalties on Healing Touch of Asklepios to 1 Wis Damage and 1d3 Subdual. Rightly, however, the Mythos Occultist doesn't like to pull out the forbidden knowledge dredged from unspeakable texts if it isn't direly required.
I decided I didn't want to totally nerf his Fast Healing, as he paid quite a few points for it (rightly so) and it DOES reduce the overall amounts of damage he deals (which is, 1d8+1d4+2 or, average, 8-9 points).
The Fast Healing IN COMBAT definately wasn't the problem, and I thought it was a great concept. Y'know, the action-movie star that gets beat down and beat down and finally left unconcious who then stands up a moment later, gets a "Second Wind" and wades back in. It was the fact that he started EVERY COMBAT with full HP while the rest of the party limped along that was the problem.
So we decided to make his Fast Healing triggered, and only active during combat rounds and for 1d6 rounds after. He's still farther ahead than others, but at least rarely at MAX from 4 hp after 4 minutes.
I'm going to look into a super-science gadget of some sort to offer additional healing between-combats, perhaps ... something for a little downtime juice. We often have 2-3 combats per In-Game Day, which is where the problem came in. I'll have to think of some way to keep that balanced.

It would be fine if we were playing just a "d20 Modern" game or just "Blood and Vigilance", but about 1/3 of the stuff we've got is totally house-rules. Quite difficult to make sure things maintain the right FLAVOR (which is my major concern) and make sure they're balanced and fun (which everybody is certainly having).
Edit: As to why so many combats.

They're pulp heroes, and prone to huge amounts of violence. Between the gang war, the super-villians, demons, cultists, super-science storm troopers, and the halloween candy force-feeding itself to them, they're usually getting scrappy several times a day during an adventure.
--fje