The fact your patient transfer service vehicles needs emergency lights is a bit worrying
I get the irony.
Unfortunately it is part of the problem in the US having patient transport fall under the auspices of EMS care.
In order to properly bill, the transport agency has to meet the criteria of an ambulance. Which is not different for emergencies or nonemergent transport.
Best described as outdated and inefficent, it is a complex issue that boils down to money.
The solution is rather simple, do not require by law an ambulance for patient transport and don't reimburse transport at anywhere near the level of an emergency ambulance. Infact I think it should be the same rate as a taxi, because that is really what it is.
You know the US system is filled with waste.