No actually flown Shuttle mission executed such a quick timeline. The likelihood of crewmembers experiencing Space Adaptation Syndrome would have made it...interesting.
Crews were trained throughout the program to perform a superficially similar timeline called Abort Once Around (AOA) which also involved landing after a single rev. But major failures were required to get into an AOA and the timeline was substantially different than the reference mission in the question. For instance, the payload bay doors were not opened and the robot arm was not unstowed on an AOA. An AOA was never executed in reality, only in simulations.
Missions actually flown executed the almost two-hour duration Post Insertion Checklist which "converted their rocket into a space station" - i.e., configured the vehicle for orbital operations. This means that major payload operations involving several crew members did not normally begin before Mission Elapsed Time (MET) of ~ 3 hours.
Here is a summary timeline from the last mission's Flight Plan showing the Post Insertion timeline.
That said, Shuttle missions that deployed major payloads on upper stages often did so early in the flight.
The most recent such was STS-93 which deployed the Chandra X-ray observatory.
The mission's flight plan is not online, but here is the planned timeline from the press kit, which shows payload deploy at ~ 7 hours into the mission in the MET column. The event is listed as DEPLOY IUS - IUS being the carrier stage, the Inertial Upper Stage, to which the observatory was mounted.
Note that payload activities are actually started in the Post Insertion timeline! The AXAF (Advanced X-Ray Astrophysics Facility aka Chandra) was powered up.
This image shows the long observatory, ready for deploy, mounted on the relatively tiny IUS (marked with USA).
The STS-70 mission which deployed a Tracking and Data Relay Satellite, again on an IUS upper stage, also had a first day deploy, this time at ~6 hours into the mission. Without checking them all, I would imagine all IUS-powered payloads got a first day deploy.