The USSC also did a memorandum ruling (I may not be using the correct phrase) for AZ in Dodge vs Graville that was based on their ruling in Troxel vs Granville.It doesn't look like anyone has cited or discussed the actual law in this thread.
Section 72(1) of the New York Domestic Relations Law states, in pertinent part, as follows:
"Where either or both of the parents of a minor child, residing within this state, is or are deceased, or where circumstances show that conditions exist which equity would see fit to intervene, a grandparent or the grandparents of such child may apply to the supreme court" to obtain a determination as to whether visitation would be in the child's best interests.
That means that, before the court even gets into a "best interests" analysis, you have to establish two things just to get your foot in the door: (1) "that conditions exist which equity would see fit to intervene;" and (2) that you are a grandparent of the child at issue.
Since you are admittedly not a grandparent of the child, that's the end of the discussion. The court does not have discretion under the law to open up third party visitation to persons other than grandparents.
As far as "adoption by estoppel," that's a concept that is used only in a couple of contexts (e.g., payment of child support and inheritance). In the former case, it is being used against the purported parent, and in the latter case, it is being used against the purported parent's estate. You are suggesting using the concept of estoppel offensively (i.e., for your own benefit), but that's not how estoppel works, so I cannot even conceive that you could use it for the purpose you describe.
As far as U.S. Supreme Court rulings, the only SCOTUS case of which I'm aware on the subject is Troxel v. Granville, 530 U.S. 57 (2000). That was an incredibly narrow case in which the Court reviewed the Washington Supreme Court's facial invalidation -- based on federal substantive due process -- of Washington's third-party visitation law. The law at issue in that case held that any person, at any time could petition for visitation with a child and that the court could order such visitation upon a "best interests" determination. Both the Washington intermediate appellate court and the Washington Supreme Court held that this law effectively allowed a state superior court judge to substitute his/her judgment for that of the child's parent(s) in terms of what's in the child's best interests. The U.S. Supreme Court affirmed this ruling and, in dicta, suggested parameters for a third-party visitation statute. In particular, it noted that a constitutional statute should limit who has standing and/or when a challenge can be made and/or should apply a standard of review beyond a garden variety "best interests" standard. Even at that time, few, if any other, states had third-party visitation statutes as broad as Washington's, and New York's unquestionably would survive a facial challenge on substantive due process ground. A decision of a New York Supreme Court that allowed a non-grandparent to obtain visitation would almost certainly be quickly reversed simply because the court exceeded its authority under the statute.