A few suggestions:

Abelia 'Canyon Creek' or 'Edward Groucher'
Wax Myrtle 'Don's Dwarf' (I have seen this at Buck Jones Nursery - call the Grayson location)

Some of the small leaf hollies like Ilex crenata might be good.

Fall is a good time to plant, but early spring isn't bad either.

Here is a link that might be useful: Don's dwarf

Abe....
Sounds like someone from the County offices are exceeding their authority! They cannot compel you to remove your fence, if it is in good repair, unless it is on the Public ROW or it exceeds the height restrictions. ( usually 4' - Front, 6' Side & Rear). If installed prior to the enactment of the height restriction ordinace, it may be grandfathered.

A permanent fence defines your property boundries and if it has been in place for many years, would help defend a property line dispute, if one arose. Living plants are not a permanent replacement.

Unless you are willing to contribute the time and expense of replacing it, I would file a complaint with the County CEO. They have a new one there and I hear that he is a BEAR, a no-nonsense type of guy!
Rb