not much help but plenty of sympathy. I've got one of those....the only time he's still is when he's in a deep sleep. He could climb the bunk ladder at 7months old so you get the idea....
I usually have lots of snacks, and lots of little toys he likes for when I need him in the pram and still.
Am a huge fan of the carrier and he's generally quite content in there as he feels a part of it. Mine doesn't do hand holding or the leash thingo either - he's just too little to understand reasoning as yet.

Is there somewhere up the front you could set up the play pen? So he could still see daddy? Now I think about this I guess it would depend on your congregation as to how they would take that.
Is there someone who can run around outside with him while the service is on?