...So, I guess it's time to mess with the voltage on the bucks. Should I just lower the buck that controls the coil or try to match both? And should I adjust them with the wires loose and no load?
So here's the thing. I've given the internal 3-terminal GM wiring some thought after your description of how they coil and light circuits interact (e.g., light dims when door opens). So I hooked up a similar configuration of components/modules myself and discovered that there is an interaction - but it's beyond me to explain in a manner which gets us to a solution vs. an arcane discussion about circuit design. And, yes, the interaction is a function of what the two regulators are set at. And, yes, the interaction is different when you share the "+" of the coil and lamp vs. share the "-".
If I were doing it (and I'm mindful that no job is so easy as the one you imagine someone else doing ) I'd throw in the towel on the shared common terminal and install a floating lamp socket. So the 2 wires from the lamp DC-DC converter output go to just the lamp. Actually, since it appears that 12V or so is a suitable voltage, I'd take the DC lamp voltage and drive a 12V LED strip and be done with it.
As for adjusting the coil voltage, in all likelihood the voltage you set with no load might drop a bit (say, 1/4V) with the coil attached. The math is somewhat complicated and depends on information not readily available (like the schematic to the regulator module). But it would be useful to know if you can reliably fire the door mechanism with 11V or 10V or whatever. As for the heating, it is what it is. That is, I think the coil is about 8 Ohms. 12V applied is a power of 18 Watts which goes out as heat. 18 Watts is a lot of power to dissipate! Consider that some small soldering irons might only use 18 Watts and they can melt solder.
But if you want to do something about the heating, I can imagine installing a 25 cent PTC resettable thermal fuse that would cut power to the coil after, say, 10 seconds (or whatever). Or there are so-called Delay-off timer relay modules (about $1 on eBay) that will open a relay after some settable time-interval (like 10 seconds or whatever). If you are just having the time-of-your-life messing with this mechanism, you might look into a "trick" used when driving perhaps the most common spring-loaded coil mechanism which is a relay itself. What happens is you apply the "full" voltage to turn the relay on, then you drop the voltage to a much lower one that is enough to hold the relay closed. This cuts relay power (heating) dramatically - routinely more than 50% reduction. Point being, I can imagine something like this allowing the coil to remain on indefinitely. But it would take some experimentation to confirm the GM mechanism would play-well with such a scheme.
Finally, when all's said and done, after all bells, flashers, etc. have been worked out, I'd re-visit the design to simplify where possible. I pretty sure this has long since gone beyond what anyone else would attempt to duplicate. But given the amount of time you've invested, perhaps there's a list of "lessons learned" that could help anyone else considering this modification.