How is solid PVA filament (for 3D printing) synthesized?
All the reactions I've seen that make PVA (also called PVOH, PVAl), create a gel-like substance that could be used as a glue or perhaps a film.


Yes, the reaction you describe is done in a solvent (water, ethanol, methanol, etc...) so that no acetate groups are unaccessable to reaction in a crystalline phase. A gel is formed because when poly(vinylacetate) is fully hydrolyzed, it is less soluble, typical white glue has about $12\%$ of the acetate groups unhydrolyzed to reduce crystallinity and keep solubility high.  The polyvinyl alcohol in filament is just dried out solid PVA, whereas the gel has water in a polymer matrix. All they have to do is melt and extrude the dry PVA powder into filament.


  I don't actually need/want it in the typical extruded filament form that would be needed for a 3D printer.  A simple solid blob of the stuff would suffice.


Side note: you can buy PVA powder online with less mess than self synthesis or depending on your application, you might be able to just use dried out white glue.