I can answer my own question now and can share the results at least for the Sisaket office.
They wanted 2 photos and 2 copies of all the relevant passport pages and visa forms......2 of everything.
The curious thing is you do NOT fill out a specific request form, think it's aT 7. You sign your name to a great many stamped pages.
The fee they collected was 2,000 baht. I was under the impression it should be 1,900 but they gave me a very straightforward receipt which my Thai friend says appears entirely proper.