Consider a step parent adoption , if bio dad wil not sign his rights away then you will have to terminate his parental rights based on abodonment. So the adoption will be a two step process.
The answers on this discussion board are general in nature and NOT intended as legal advice. Responding to questions does not constitute an attorney-client relationship. Always see a lawyer about your individual situation.
The first step would be to ask the father if he would give up his rights so your husband could do a step-parent adoption. Use the fact that he (your ex) would no longer have to pay child support.
If that does not work than you would need to petition to terminate the rights of the father.
Note this answer does not constitute legal advice, and should not be relied on. Each situation is fact specific and court specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship
I agree with the Step Parent Adoption suggested by previous counsel in California after a year of no contact you can file for severance of Parental Rights based on Abandonment within the Step Parent Adoption proceeding. If of course he does file a request for custodial rights and visitation you will have a more difficult time preventing him from exercising some type of visitation,but if he has had little contact as you say any court would take baby steps with custody and visitation orders