I had to jump through a bunch of hoops when I built my garage...

I ended up having to get an attorney when I closed a paper alley that was the rear boundary...

You mention the setbacks are 10'... I know where I'm at they are 8' to a side or rear property line owned by someone else...

In my case it was a county owned paper alley which had a 15' setback...Thus the need for an attorney...

I think I'd run the new property line between the two where both owners mutually agree it needs to be and have that drawn up to approach the county with...

I'm not sure if including the location of the existing structure would matter as your only concern with the county would be the land acquisition...

In my experience with the county they do not answer questions directly for fear of being held to what they say...