The reason I asked where you were located was because their might be someone on this board that lives near enough to you that they could come by and give you a hand once you are ready to do the actual work.
I'm three hours away and if I was retired, I'd drive over to Memphis and give you hand - unfortunately, I'm not retired.
I'm surprised at the local inspectors attitude regrading your hiring an electrician, but it is what it is.
Once we figure out what size wire you need, I can check with my local electrical distributor - they have a location in Jackson, TN that you could pick it up at, using my discount. I know that's a bit of drive, but it might be worth it for you.
Can you post a sketch of the house and garage locations and maybe some pictures?
As others have said, IF you need a true 200 amps available in your garage with acceptable voltage drop, then you will need large than 2/0 (2 "aught"). It is quite possible your meter base could take a smaller breaker to feed your garage (150 amps say). This would allow you to run 2/0 (2 "aught) to the garage. We should do some price comparison on different size wire to see if the costs justify the 200 amp service in the garage.
150 amps is a lot for a garage, even one with a lot of equipment in it.