You don’t say how far your wife lives from you. If she is relatively nearby, why go thru the expense and trauma of a custody hearing if your wife will let you be more involved in your son’s life. He doesn’t need a custody battle – he just wants to be with you more.
You say the home inspection will render this a no contest. Guess again.
This forum and the newspapers are full of reports of children living in absolute filth and still being returned to the parents. Your son needs to be able to articulate, in a manner appropriate to a 12 yo, why he feels it is better for him to be with the father than with the mother. You can’t coach him – the judge has seen it all – it has to come from the kids heart.
And remember, mom isn’t likely to give her son up without a fight. If she promises to improve living conditions, the judge may rule against you.
There are no certainties in life but death and taxes. Have you considered an alternative win-win solution for all concerned? I don’t mean to burst your bubble but don’t get too cocky.