How long does it take to process a request for an extended stay after submitting the required documentation in Thailand?

The problem isn't the time after you've submitted the papers, but getting all of the right papers. And the queue for delivering the papers.

I've only ever waited like 30min max after being shuffled into the waiting-room after delivering all the papers. And that was on what I feel was busy days.

Done this in Bangkok twice.

Depends on the office you’re going to be using. Approx 20 minutes turn around for most I’d guess. Actual time it takes to get the extension overall will be governed by the number of people in front of you queueing to do the same.