What is the process for applying for a Non-O retirement visa and 90-day reporting in Thailand?

I believe you are confusing getting a year-long, multi-entry Non-O visa from a thai consulate in your country BEFORE you come here <- which gives you just a 90 day entry stamp and then you bounce out and back to get a new 90 days (and you do that for the whole year)

With coming here and applying first for the 90 day non-O visa and then the yearly extension with a re-entry permit inside the country at the immigration office <- which is the way you can stay a year and do 90 day reporting.

They are completely different processes one done BEFORE you come here, one done AFTER you come here.

You are talking about doing it ALL after you come here, and it's your terminology that is messing you up a bit too

There is no year long, multi-entry Non-O visa sold INSIDE the country.

1 - You apply for a 90 day no entry Non-O visa for 2000baht (it has no re-entry because you're already IN thailand when you apply for the visa)

2 - you apply for the year extension for 1900baht when that 90 days runs down,

3 - you apply for a re-entry permit after you get the year extension inked in (1000baht single, or 3800baht multiple) then you can exit/re-enter all you want and you will be doing 90 day reporting NOT bouncing out and back to get a new 90 day stamp.