Just a quick update. I finished reassembling the extruder last week. Compared to the old raygun, the new one has a few notable changes. The heat sink's closer to the heater block, to try and reduce the coefficient of friction between the walls and molten plastic. The leads of the resistor and the thermistor are insulated within concrete, so they won't short to the heater block. The cooling fan's fastened on better. Most notably, the hot end of the hot end is now swaddled in fiberglass - bona fide insulation.
On the bright side, the hot end performs like a champ. Only the lower two washers of the heat sink were warm, and the heater block came up to temperature with much more authority than usual.
Unfortunately, it still doesn't work. I tried an extrusion yesterday, to no avail. The printer produced a few sickly-looking brown blobs of plastic (my filament's white), but refused to extrude filament.
Possibilities: The acorn nut is clogged up past the point of usefulness - burn it clean with a torch. The plastic's still melting too early - add a thermal barrier of some sort. The plastic isn't slippery enough - add oil (sounds silly; some have had luck with that route). The cold end doesn't have enough traction - add more pressure.
I'm leaning towards the acorn nut - it's been jammed in the past, and I'm not sure how wide its 0.35mm hole is right now. Switching to a 0.5mm aperture is a shot in the dark, but might work.
As another possibility, I could feed the printer 1.75mm filament. That has less volume per length, so should feed with less pushing power.