So I came across this video today:
It shows how a production injection molding machine works and the history of the older styles of injection molding machines like out hand operated machine.
The present commercial machine uses the compression screw like the injection molder, then the screw itself is moved forward like a piston to inject plastic.
What instead if the extrusion machine filled a chamber with molten plastic and then a separate piston injected the plastic? this would greatly simplify the process and enable a much lower cost production machine.