I managed to get the freezer back cover off (which was by far the hardest part, even following a video tutorial) and as expected, the coils were totally iced over. I followed another tutorial to check things with a meter and the heater and defrost timer circuit came up as expected. The thermistors were a little off, reading 13.3k Ohms when they're supposed to be in the 16 area, but the evaporator and lower freezer area thermistor were both similar values while submerged in ice water for a few minutes so either both are okay or both are contributing to the problem.

I went ahead and defrosted the coils with a hair dryer and sealed things back up and temperatures are reading normal again. This issue may have been considerably longer term than I initially thought: I had (what I thought was a separate issue) a problem with the top half of the freezer sometimes getting warm enough that water droplets would condense on the roof of the freezer and food would thaw out sometimes. That problem is now gone.

Anyway, temps are back to normal and have been holding there for the past several days so I'm hopeful just that bit of maintenance is all that will be required.