For additional height, would it be possible to be creative in your footings and slab?
I am projecting that you have a basement or crawl space which raises the height of your 1st floor 2 ft above surrounding grade. If so, pouring your footings so the garage floor is ~level with the house floor. But don't pour the slab (at this time). Use gravel as your garage floor and finish the build through all inspections with gravel in place. When they (inspectors) ask why you opted for gravel (as a possible answer), you are strongly considering radiant floor heating in the future but you are undecided about all the variables at this time and don't want to waste the cash by rushing into an incomplete design so you are utilizing gravel for the time being.
After, your garage is complete and fully inspected. Remove the gravel down to the appropriate grade and pour the full driveway connection (i.e., slab and connection to your driveway). You decided against radiant flooring so you are finalizing the flooring. This potentially could gain you a couple of feet in additional interior height. This would add cost for the extra gravel, out of sequence work, added work and your man doors would need steps (interior and exterior).
With the city being inflexible and painting you into a corner with rules, a creative design and flexible approach are elements that you might be able to introduce to get closer to your dream. This is only an off the cuff concept on my part, so there are probably many other flexible creative concepts that you might explore.
Good luck.