MotorSeven,
I did site management on 2 to 6 million dollars construction jobs in the 90's. I agree with "no way" especially if you consider that with your 27" drop, an 8" deep footer won't be on virgin soil (which is normally non-negotiable).
I've been on commercial jobs where engineered fill is used under the floor slab, it's laid down in repeated thin 2"-3" layers and compacted with vibratory rollers and checked for percentage of compaction with proctor tests. With all that, the engineered fill is only good for the floor, footers ALWAYS go down to rest on virgin ground, I've seen them up to 8' deep.
Another way to support a bldg floor is to have holes augered down to solid ground for your base, you can even tie them together under the floor with grade beams (picture holes around the perimeter of your floor with a 12" , or whatever size you need trench connecting them across the floor). Rebar, or sometimes an I beam in the trench will create a reinforced concrete beam under the floor when filled w/concrete. This is probably overkill for your application but I'm just trying to show you how seriously support is considered in commercial construction.
Another technique you can use to stiffen a floor is a haunch, it's similar to, but not as involved as the grade beam. A haunch is just a section of thicker floor, usually running from side to side, typically something like 8" or 12" wide and double the floor thickness.
I'm working on a 4" floor slab for a 24' x 40' garage for my brother now, we're going to pour it monolithic, with a 12" hole augered 36" deep every 8' around the perimeter, rebar in floor on 2' centers with vertical rebar in holes tied into floor rebar. The holes replace a continuous footer and save a substantial amount of concrete, but they are directly under the bearing walls and tied into the floor rebar. Haunches will be placed in an area where he is planning on placing a hoist.
Forming a floor the way I described is more involved than a regular footer, but, using the same (or even less) amount of concrete, can be made much stronger than a traditional continuous footer. Essentially, it's a modified and improved pole building foundation, but instead of a dirt floor, the concrete floor has rebar reinforcements connecting all the holes together.
If you use the holes for your footer you should always put a haunch at the garage doors where equipment is coming on and off the floor. My garage has a 12" x 12" one at the doors.