The 'drain defrost install' is done, thank you very much denman! You made it easy enough that even I, with little mechanical ability, could do it.

I've forced a couple defrost cycles (once after letting frost build overnight), and while the frost on the evaporator and wire melts, and neither remain cold, not only is the wire not too hot, it doesn't feel particularly 'warm'..but then neither does the defrost heater itself. I guess in a couple days I'll know for sure whether the drain remains clear now.

p.s. I was surprised to find that instead of the 30-minute defrost period the manual listed, it only lasts 15 minutes.

In (each time about) 15 minutes the compressor actually turned back on. (I honestly don't know what "compressor" means, but in context I gather that that's the loud component that freezes the compartment.)

Now 6 weeks later, the drain continues to remain clear. Just a little more buildup on the path. Perhaps after many months I will need to use hot water (which before this fix I had to use every other day). I couldn't be more happy with this fix, thank you again, denman!

hoping to piggyback my question onto this solution, since I have the same problem with my GE GDS18SBR/LBR. like clockwork my drain pan will collect enough ice to block the drain hole in a week.

first I tried loosely coiling copper wire (probably 18 gauge) around the defrost element and draping it down the drain, didn't work. then, since the drain pan under the evaporator is a separate piece from the part that funnels the liquid to the drain I installed a tube directly from the drain pan to the drain hole, also didn't work. I ended up coiling the copper tighter around the element, wrapping it in foil, then draping a strand of the copper through my custom drain tube. worked great for a couple months but now I'm back to a weekly manual defrost schedule.

has anyone been able to troubleshoot this kind of problem to a specific part of the system? I know the defrost timer and element work. if the thermostat has any kind of failure it isn't keeping the element from turning on. is there an expansion valve that could be leaking causing the drain pan to be warm enough to melt at the defrost element but cold enough to re-freeze at the drain?

I am assuming that the evaporator coils are defrosting properly and it is just a drain problem.
Also that the drain line is clear. Could be that gunk has grown in the drain line and is slowing down the draining so even with with a drain heater you still get drain freeze ups.
If it drains slow then flush the drain line with a 10% bleach solution.
This should kill anything in the drain line and let you flush it out with warm water.
A turkey baster comes in handy when doing this.
Just take care that you do not overflow your drip tray.
Also wear old clothes unless you are into bleach designs on your clothes.

I am not sure why the drain heater wire is gray.
I would also replace your drain heater.
Check that the defrost heater looks OK where the drain heater is wrapped around it.
Clean it if it also has gray deposits.

Then I would let the unit cool down again and force a defrost cycle just to be sure everything is working OK.
Be careful to not burn your fingers on the defrost heater.
The drain heater just has to get warm.

The evaporator coils have to be frozen or the defrost thermostat will not be closed and this kills power to the defrost heater.