... judge might say: "I don't believe that either side has made a major case, but it won't hurt the child to see grandma, so I'll order some level of visitation for grandma"...
Given this case is now headed toward trial, this is a very real possiblity you should be prepared for. I would not presume this is an open and shut case for you.
Although you may have looked into case law that supports your position, you need to research both the relevant statutes and case law that support the GP's position in this case. Because that it the direction she and her attorney are coming at you from.
Granny would not normally be granted a trial on the merits unless she had enough of a legal fingerhold to sustain this suit. And such a fingerhold requires meeting a statutory threshold. Otherwise it would have been dismissed. So you need to understand what the relevant statutes are that got her a trial, and what they could mean in the context of your case.
While case law can be important, don't get too hung up on it, especially in family law cases, because cases arising from appeals address specific points of error in the interpretation or application of statutes, or their constitutionality, as applied to that case. These cases serve as guidelines to clarify any confusion or ambiguities in both the letter and intent of the statutes. But ultimately, the plain letter of the statutes rule.
Your case is not a case where one side has no evidence at all to support their position. Each side will offer evidence from expert witnesses, their own testimony, and more. It is entirely possible the judge already knows both expert witnesses from prior cases and may already have formed an opinion on which one he is more inclined to believe.
Given this, and if the statutes are written such that it gives the court the right to decide on visitation in your case, it could go either way.
Not trying to bum you out, because it could very well go in your favor, as it should.