I looked at how much wider the stock tires are compared to the spare, and it's a few inches... more than that tray thickness. Hm, but you say 3" deep - you must have the hatch version that has a handy storage bin there... wish my 4 door had that.
You can melt / cut the area out to get some extra space, though I think you'll still be higher than the rest of the floor. Way back i'd looked into it, and it doesn't seem that the bottom side can be moved since the rear subframe is right there...
So live with an uneven floor - or some kind of your own mod, like a 4-5" deep tray with the tire in the middle. Good luck.
Dave '07 M3 GT, manual, - black
Adders: backup sensors, current limited hi-beams (for long life), Fog light on with running lights (t=44332 PAGE2), low beam aiming switch adjustment (t=47722), dash squeak reduction, badges removed, door bumpers removed, auto up/down windows, under seat subwoofer, True hidden hitch (t=53213), rear camber fix (t=53425)
Info / help: outside running lights only as DRL (t=54453)
link example http://www.mazda3club.com/mazda3-mazdaspeed3-98/drl-my-corner-lamp-54453/