I would look into adding on to the home as well. If you can build a workshop that is say 14 wide X the length of one wall, say 20 or 30' that will give you a lot of space for a workshop. You could build it like a screened in porch or something? You can buy 2X10 that are 16' long for the roof, and then adjust the wall to where you will need it to fit under that roof.
This should increase the 'house' size by 280 - 400 square feet.
With a 2,800 square foot home, then you could be allowed a 1,400 square foot roof for the RV garage or whatever you wanted to build.
If the county will not budge on the RV garage, my suggestion is to see if they require a permit to build a table and chairs. One horse owner posted on Facebook their 12' tall table and 14' tall chairs, due to county restrictions about a horse structure! Tell them that you are expecting Paul Bunnion to show up for dinner, at least you have him invited over.. .
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Good luck,
Fred.