Can they legally hold me to this lease under these conditions?

You signed the lease, moved into the property, and paid rent. So, you have a lease. The co-signor does not matter, nor do other "guidelines" they prefer to follow as those are not legal requirements. You have a lease and you are responsible for the rent until the end of the lease, whether you move or not. You can move, they can sue, you can pay or not, but you will be hounded for collections and have your credit ruined. Best to just stay through the term of the lease.