In early July, I applied "electronically" (but had to bring a hard copy of my training cert) at one of the regional license locations (Orlando), and it took only three weeks to receive my permit.
However, that was after a two month wait for the appointment. I called to make the appointment in May, and early July was the earliest date available.
The process took about 25 minutes total - split between completing the electronic application at a computer, and getting electronic prints & a pic taken.
They could have easily handled two or three more applicants at the same time. One applicant was leaving when I arrived, and one or two showed up while I was there, but they were still in the waiting area as I left.
I was told - and there were signs posted several places - that it could take up to 90 days to receive the permit. The status could be checked online, but I never checked it, as I received the permit sooner than expected.
Overall, a simple & painless process, except for the 45 minute drive I had each way (my car has no A/C).