Scout, sorry I was not following the details of your sitch. I thought you were trying to avoid or couldn't afford lawyers and court and didn't know you had finances done. That is awesome! So amazing!
In that case I don't know why you are trying to push anything forward. If he is asking for very little access, I would not push it at all! The status quo will probably prevail in that case.
I used to try to ensure my kids had their dad in their lives. Now I see it differently. My son was suicidal, shoplifting, school refuser til I finally paid his dad to move out. Slowly but surely, he got better and better. He hasn't seen his dad in over a year and is really growing into adulthood, taking school more seriously, earning his own money, has happiness and hope, no more depression, much less rage, helping me more, etc. Meanwhile, his sister sees her dad (whenever he is not moving from state to state) and talks to him a lot, a lot of middleschoolesque texting all day, a lot of him criticizing me and vaping and drinking in front of her, other woman talk or present, etc., and my daughter is a MESS. She used to be my easy child, a little angel. Now she is always confused and anxious and lashing out and unfocused with school, fighting me to wear sexy clothes at age 10/11 and has even been cursing, hitting her brother, etc. I think she is depressed and she is definitely self medicating with food. Some of that is tween stuff I know, but the degree is very intense and a huge change for her that coincided with H suddenly taking an interest in her last year.
You don't want to be seen as standing in the way of H seeing S, I agree, but I don't think you need to push it either.
I believe I will see the bounty of the Lord in the land of the living. Wait for the Lord with courage. Be stouthearted, and wait for the Lord.