I volunteer with some storm clean up groups - can't low ball much lower than free. Photo posted is probably a homeowner or neighbor doing what they can with what they've got.
Some for profit tree services don't like us showing up and helping out, even though, right after a storm there is lots for everyone to do - they feel that we are cutting into 'their' profits. When we have time to talk to the established tree services who really work in the affected areas, we usually come to a quick understanding: we are mostly doing ground clean up, removing trees and limbs from driveways, sidewalks, off lawns, etc.
We leave the larger and technical stuff to professionals who have the training, experience, and equipment. By taking care of the surrounding stuff, they are able to get to the technical stuff more quickly and focus on that. They get plenty of work, and the neighborhood gets cleaned up faster for the residents.
The guys who run around and try to sign everyone up and collect deposits for work that they can't get to for days or weeks really p --- people off. Along with price gougers, and outright rip-off guys. Residents get tired of people ringing their doorbells every 5 minutes (if they still have power).
Don't know you personally, but sounds like you are legit and established in the tree care business. Your skills are needed after these events, and if you want to work, there should be plenty to go around. Emphasize the experience you have, along with any licensing and insurance in a brief flier. Don't oversell or make promises about what insurance or FEMA might cover. Could be some sub contract work with other established tree service companies already on the ground, and could be work from homeowners tired of waiting for the fly-by-nighters to return.
Philbert