Extruder gear access door screw is tightening  

Simple answer is no.  How have you determined that its self tightening ? Filament grinding after a few hours is a normal sign of heat creep leading to the grinding but I have never seen anyone post that the screw has gotten tighter on its own.

I cant see how that is even physically possible given the design.

The head is more recessed

I am surprised it is tightening as well.  I can tell it is tightening because the head of the screw, which is normally about flush with the outside of the housing, is more recessed.  I can also see that the end of the screw is protruding more out the back side of the nut.

As a result, I've had to check it before starting a print and sometimes back it out.  On a longer print, which I haven't done since noticing this, I may have to back it out mid-print.

Haven´t had the problem myself.
A possible fix, if the screw protrude from the nut, is changing the nut to nyloc nut
BUT, 🤔 my screw does not protrude from the nut at all, more like screwed in less than 2 turns in the nut

My bolt is a duplicate from the spares

Hmmm.  My original bolt bound up in the nut; when I tried to unscrew it it rounded out the hex hole for the nut in the door.  I had to saw off the bolt to replace it.  So the current nut is free to rotate, but I would think any rotation would be *un*screwing, given the spring tension on the bolt.  I have printed a new door but haven't installed it.  I'm pretty sure the replacement bolt is the same length as the original.

Is your bolt head flush with the housing, more-or-less?  If not, how did you adjust the pressure to an appropriate amount?

@ga

The bolt head is 2-3mm outside.

I autoload filament with screw as loose it could get without falling out, then tighten it until the filament start to extrude without clicking. Never touched it after that. 

If the nut is free to rotate that would explain the movement, your printer is not as it’s originally designed. If you already have a replacement door printed then I would fit it. It does not logically follow that the spring will cause it to loosen, it all depends in the order of pressure.

Need to pick up a 3mm drill bit

Thanks.  I haven't put it on yet because I need to pick up a 3mm drill; the bolt and gear shaft holes are a bit under-sized due to filament squish, I presume.

Screw should stick out past the nut ...

Whomever's picture above with the screw barely seated in the nut - I'd advise a few more turns for PLA/PETG/ABS/ASA.   For TPU, your picture looks right.