Most of us have been through this. Have your vendor end the contract. Take two weeks off and then start full time. In the mean time block all communication with the consultancy. Do not reply any thing over email, from their "lawyers".
Legally you have to be served to be sued. That has to happen in person.

They also have the burden to prove their losses. In this case, your contract ended at the end of project. Depending on the state you live and work, non compete even may not be enforceable. They cant prevent you to work and earn a living.
INAL, accept employment, take two weeks break. Then ignore all their calls.