HI Larry,
Strange they won't permit a new house since it increases the tax base?
Maybe increase your own home value by petitioning the local government to close and abandon the alley and deed it over to you and your neighbor, (though it would still probably remain an easement).
Then fence the whole of your property as one unit, and sell it as a large lot property in the city.
Also, most of these empty older city lots had a home on them at one time that either burned or was condemned.
When they razed a structure in the old days they would just push the debris from the house into the foundation and level the foundation to just below the dirt.
Meaning there might be a full basement there just below the grass (full of debris), that might qualify as a rebuild or an addition of sorts, instead of new construction.
If they allow this, you can look for the old basement by driving a rebar at a 45 degree angle into the dirt after it rains. Start from the front of the lot and go backwards.
Good luck!