The way you share custody with a non-parent is through guardianship. I discussed how to look into that (feel free to ask questions). You do not want to give up all custody. I would check into his insurance though, I'm not sure you can get them covered this way but you should surely look into the policy if you want to try.
PS: While I know you trust your father, there are so many bad possibilities. He may acquire a new wife who influences him, he could become incapacitated and you don't automatically get custody back if you gave it up entirely, he could die, any number of bad things that could complicate matters.
Go the route of guardianship. Talk to an attorney to do it right, it won't cost that much.
I just re-read your post, I don't know where I got the idea that you wanted to give up all custody to him. I read and answer a lot of posts. Sorry.