Why do you think your ambulance is some kind of sacred medical Mecca that should never allow patients to rest? The man is 94 years old. He's being transferred for a routine non-emergent issue, and your role in this scenario is to provide a comfortable and safe ride to the hospital.
I didn't insinuate that you were burnt out, nor would I ever suggest that IFT services don't provide good care. Furthermore, differences between 911 and IFT has nothing to do with this scenario. The reality is BLS IFT should emphasize transport and good customer service. In this case, good customer service means letting the patient sleep. You're not going to do anything to fix the patient's medical problem, and any questions you want answered are in the patient's chart right in front of you. The sending facility likely called in report to the receiving anyway, and telling the receiving RN that your stable patient slept comfortably without complaint for the 15 minute transport with stable vitals throughout is perfectly acceptable. Pass on the chief complaint and chart, and your handover report is finished.