Here is a previous post on towing a RWD vehicle backwards on a dolly. While towing backwards is not as stable and I would not recommend pulling it with a PU but behind a MH it is doable.
I'd go and rent a dolly and try it by locking the steering wheel straight with the seat belt. Without any traffic and at increasing speeds steer the MH quickly L/R to see what happens. Once you prove it's stable you are going to need some type of braking on the Mazda if you do not buy a dolly with brakes.
Let the "OH NO's" begin by those that have never done it. One of my favorites is about caster and camber. You might want to click on "How I Tow" below. :W
