The father of my son is incarcerated in Sing Sing and won't be paroled for a long time. I would like to obtain full custody of my son. Do you think the request will be considered?

You currently have full custody because the father is "away." If you want to make it legal for some reason you can go to Court but I don't see any purpose behind that.

If you get full custody now the father can attempt to get it changed when he is released.