Question for energy_rater_La and others

I had indicated a desire to remove my drywall vaulted ceiling, R-19 batts and replace with closed cell foam. Yesterday the insulation contractor came out. He recommends only open cell foam saying he only likes closed cell in walls. I only have 5 1/2 inches and really don't want the ceiling lowered (furr). Open cell wouldn't give me much more than R19 which I have now. I suggested 2 or 3 inches of closed cell and the rest open cell. The contractor said that would double the cost. Not sure what to do.

Suggestions are appreciated.

BTW, I do read James Lee Burke and will plan to visit the restaurant in New Iberia next week. Thanks for telling me about it.