Oh, my system would be amazing.
It would be divided at dispatch into three tiers- transport, ambulance and Team Kia. Transport would be wheelchairs, the dialysis derby, etc. Lump in a few BLS transfer trucks with EMTs for stable interfacility work. Overtime would be as manual labor for various image-building events and company work like cleaning the building or whatever.
Ambulance would be entirely emergent IFT, patients who actually need medical supervision for whatever and my pride and joy, a large 911 ALS/CCT section staffed at 1 truck per 5-10,000 people, station-based, with multiple trucks per station. This would be an epic 911 system with a lot of amazing tools, drugs to make an ED jealous and such, but it would functionally resemble what we do today, just better. Protocols would be outstandingly awesome.
Team Kia would be a single medic, EMT or potentially an MA, in a car, with a telemed suite connected ted to an on-call physician. Some meds, basic tools, and prescription pad/digital prescriptions. Essentially a mobile urgent care.
All calls and requests for service are screened at dispatch. Calls that need an ambulance get an ambulance, transfer calls get the right vehicle. Calls that don't seem to need an ambulance get Team Kia. They show up, assess, do a telemed remote assessment and consult, see if they can fix the problem and bill it as primary care to insurance or cash at service. Patients who can't pay get appropriate EMS care but won't get to enjoy Team Kia's awesome service. Team Kia basically offers the sniffles some basic primary care.
A physician or PA or NP would be on duty at dispatch for telemed.
Pay would be extravagant, deliberately more than any other area private service in the area, often more than fire.
The catch? I'd only hire people who could identify a flaw and present a solution.