I don't know if my experience applies to your DH. I am very thin, and chest muscles are weak. However, DS naps quite easily on me if I wear him in a MT (front carry), despite wife has far better "cushions".
When it's close to time for a nap and I am wearing DS, I will stop talking, take a good walk outside (around the park, the pier, etc...or just the pavement if there is no choice - but I hate the noise and air pollution) and walk very steadily (non-stop). I will pat his hip lightly to aid him too. Normally he will fall into sleep in less than 10 minutes. Then I can sit down (e.g. on a chair in the park - but make sure that no one is smoking or shouting beside) and enjoy a book's chapter or the sea or just feel the little one's breath.
I do this almost everyday for DS's third nap (late afternoon). For his first and second nap, I use a sling and wear him down to bed (previously after he entered deep sleep but now just put him down when he is sleepy). He is now 7.5 months and I have done these daily for 5 months.
I think the cue is to let the baby get used to Daddy's difference and accept Daddy as the comforter. So just keep practise! (and tell your DH he is not alone !