I bought my house 8 years ago, a 1920 Colonial. Less than a year after
purchase, the city declared the neighborhood a historic district with
no input from the neighborhood residents.

My biggest problem is that one of the 150 year old oak trees on the
street in front of my house lost a major branch in an ice storm last
winter. The city came out and took the tree down, in the process part
of the tree hit my house and broke about a dozen slate roof tiles. The
city mailed me a check for $ 500 for repairs. I contacted every roofer
in the phone book, the low bid was $ 5,000 (10X what the city said it
would cost). Knowing that the roof has to be repaired, I okayed it and
the roofer went to the city for a permit which they denied. Said that
the slate roof was 85 years old and new slate would not match and I
would have to completely reroof the entire house, estimate $ 100,000.
This would be okay, except the house with a new roof would only be
worth $ 75,000 (okay, so it's not the best neighborhood to start with).

I have requested an exemption and been denied, any other solutions?
There have been 3 homes already abandoned in the neighborhood as the
repairs cost more than the cost of a functional house elsewhere.