I don't think this fridge has an evaporator fan that moves air from the freezer to cool the fresh food section.  I'm pretty sure the cold plate in the back of the fresh food cabinet serves that purpose.

This sounds more like an issue with a blockage or leak in the sealed system, which would be a real drag if that's the problem.  As the OP stated above, these days a so-called repairman -- likely less than half the age of the fridge itself -- would quickly dismiss it as not worth fixing since it would be far beyond his minimal scope of capabilities.

Good to know the issue seems to have been resolved.

I'm a big fan of GE Combinations with revolving -- or better yet, swing-out shelving.  Defrosting is an easy job thanks to the drains GE provided in the freezer sections, and GE also designed the cooling system for the freezers so that only the top and rear of the freezer accumulates frost.  This means freezer contents never get coated with much, if any frost.  It truly is the next best thing to frost-free, without the marked increase in energy consumption.

Here's a link to a source for door seal gaskets.  You can order a sample ring or try to match what you have through images of individual types.

I think someone recently posted a link to another source, but I can't find that thread.

I replaced the freezer gasket on my GE Combination and it made a world of difference.  Defrosting intervals went from every other month to less than twice a year.  Granted, that fridge wasn't my daily driver so the freezer could go for days without being accessed, but a new door seal will certainly decrease the frequency of your defrosting jobs regardless.

Restriction in the sealed system. Moisture?