I have fire blight (almost positive) on two full grown crab apple trees. It has spread over much of the trees. Is the recommended solution to cut down the trees? If so, can I drag the cut trees deep into the woods for disposal?

Very sad about the crabapple trees.
Fireblight is extremely contagious to all species in the Rosaceae family. Do not dispose of the infected growth in the woods. Burn it if you can, cut it up and dispose in the landfill, or consult your local agricultural extension office for advice. This article about control won't help at this point but it does list several sources that might be useful
https://ag.umass.edu/landscape...

Comprehensive info if you need it
https://extension.umn.edu/plan...