How to proceed with a supervisor who won't read paper manuscripts? But won't allow submission until they have read them?
Your supervisor's slow response rate is clearly holding you back.  It's time to talk to your department administration about the problem.

When you do so, please state the problem in neutral terms.  Examples of things to leave out: This individual tends to over-promise and then not deliver with external funding bodies....  It has been myself and another who have always come through, at the expense of our personal (unpaid and recognised) time, for the good of the group's image.  That may all be true, but administration will probably respond in a more useful way if you can keep the emotions out of your exposition.  (This is not to say that I don't understand your frustration.)

Meanwhile, please find at least one knowledgeable and trustworthy person to show your manuscripts to, so you can get some useful feedback on them.