What are the procedures for applying for Permanent Residency (PR) in Thailand while on a Non-B visa?

You will hit the required 3 years here on unbroken yearly extensions of stays TOO late to apply this year :(

You have to have the 3 years of unbroken extensions when you FILE your application

Unless you did all your paperwork and then held the application until the last moment you will have to wait until next year

They have no even opened up the applications for PR yet.

GO out to Chaengwattana Immigation office and talk to the people in the PR application area. They will give you the hand out that lists the documents you need, how many of them etc, and they will also tell you IF you can apply this year or wait for next year.