Water cooling would simplify things a lot and you can always do a dry off and then bake in a oven or use water absorbents  to dry the produced filament. Water will enable a  skin to be quickly formed locking the diameter  Besides it only needs to cool down and then be  dried and rolled up a matter of seconds, There wouldn't be that serious an amount of water impact in that time frame. Of course you need to then dry it of for best performance. The above design direction is no god for other reasons, first you have a large amount of  plastic with poor mixing so you get solid s and partial melt  and you will get crystallisation if it sits there  for a long time producing poor product that fractures and lacks strength. The screw extruder idea is neded  and a design with a  flow valve arrestor. I dont think a conventional   spiral wood drill will work as well as a  specially ground  exstruder but possibly

As I understand the key to constant filament diameter is get consistent force driving the plastic through the whole extrusion. I have seen a plunger based version of this before and they had problems with the beginning and ending of the stoke causing inconsistency. In your system I could see that the amount of plastic above the melt point would changing This might change the the driving force with the amount of filament above the melt point as so have a similar problem.

I am not really sure if this issue since the temp might have a much larger effect.

Regardless I love this initial design.

I had some similar thoughs, except never got around to building a test rig... For the filament collector/spooler, my idea was to have a large circular tub of cold water and have an X and Y axis on the filament extruder and to move it in a large circle around the inside of the tub while it extruded. That way you'd end up with a large circular spool of filament without as much trouble from having pullers and the like, which might affect filament diameter.

All still a bit of a thought experiment for me though...

Wow, very interesting. I was working on something that looked pretty similar. Except I was going to try using air pressure to for force the plastic out. Never finished because it kind of seemed like having a closed, pressurized system would be to difficult to add more plastic to melt to. Instead I have been looking for an old style meat grinder to try an auger driven extruder instead. I may have to try a gravity fed setup.