Yeppers. IMHO, that last one is the key. The DPS has 30 days to get the app to the the "director's designee." That designee (e.g., the county-of-residence Sheriff's department) has 60 days to get a response back to DPS. DPS has a total of 90 days to tell you something: either yea, nay, or need more time for research. Kicker is that the statute says if they don't tell you anything at all after 120 days it means you are automatically denied. Nice grass-catcher bit, that last.then...411.177.......
(b) The department shall, not later than the 60th day after the date
of the receipt by the director's designee of the completed application
materials: ...
I fully understand the DPS doesn't control the "director's designee." To DPS's credit, even their voice prompt when you call says they try to handle all applications in 60 days. And I think they do a pretty good job.
But you are completely correct: there is no legal requirement for them to issue or deny within 60 days of the receipt of the application.