I signed a business contract as a contractor under my own name. My husband and I want to form an LLC as protection instead.

You can contract with the LLC for it to assume the contract, but that would only affect your rights vis a vis the LLC.  In other words, you could sue the LLC if the other party sued you, but given that you would own the LLC, that doesn't mean much.  You can't impair the rights of  the other contracting party (to hold you personally responsible for the contract) without that party's consent.