Hi Katy,
The problem with mounting a spare tire on the front of a vehicle is you block the airflow to the radiator and risk overheating the engine, especially with something like an ambulance which already requires an oversized radiator and transmission cooler.
You can build a rack and put it on top of the cab, which a lot of people do, but then you have to figure out how you're going to get the 78 lb. stock tire and rim up and down. That doesn't sound like that much weight, but try climbing with one hand and holding the spare with the other hand. So, that leaves building some kind of winch assembly to raise and lower it. Of course if you will always have two people available, then it wouldn't be that difficult for a stock height vehicle.
The rear door on a swing away carrier is a good location, but can be a pain moving it everytime you want to open a door.
That leaves one location, which is underneath in the rear as if it were a van or PU Truck. I have two ambulance bodies which I am converting into camper trailers. I started with a 1993 Type III Wheeled Coach and moved up to a 2005 Type I version. The 1993 model had the spare located in the rear between the frame rails like a van has, but the only person who was going to remove that spare was an experienced mechanic with a pneumatic impact wrench and possibly a cutting torch. The was no winch assembly to lower the tire, only a long 3/4" diameter bolt which ran from the frame down through one of the lug bolt holes, with a big washer and nut on it. The bolt was bent and the threads were stripped. It took me two hours to get that tire and wheel out from under there.
So, there are the options as I see them. The rack on the cab roof is probably the simplest and cheapest, providing you have the manpower to get the spare up and down. The rear door option will be expensive because you can't just go to Walmart and buy a swing away spare tire mount for an ambulance, it will have to be custom built. The underframe option would provide easy access to the spare it you can find a spare tire winch assembly for a van or PU truck and adapt it to work under there. Mounting it on the front would be relatively easy to do, however I would only use that method as a last resort due to the possible overheating problem.
In answer to your question, there is no correct answer... Basically, it's going to be a select the 'lesser of all the evils' and go with that plan.