If the heater failed, that would solve all this... as would disconnecting it, if you call it a solution to have to manually defrost it. If the control board isn't cycling the heater on, no water production, correct? If it is, then it seems to be working? Without owning the fridge, it seems more like the drain is poorly designed and may have built up some residue (fugus) that slows water flow too much, assuming it did not have this problem when new?
There is only so much alteration to a bad design that you can do, since it seems this is something that happens without a specific failure?
There are some film type heating elements that you could strategically place to run in parallel to the defrost heater (mounted to sheet aluminum if heat density is too high), but that's quite an experiment to do with one's primary source of cold food storage.
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