I would check with your pediatrician, but I would do it in the opposite order - change bedtime first, break nighttime feeding second. Obviously all babies are different, but I think the goal is to shoot for around 12 hours of sleep a night. Since your LO sleeps for less then that I would try to change the bedtime first and get him sleeping earlier and for longer stretches, and then once he's got that down break the nighttime feeding. How many naps does he take? What time is his last nap?
FWIW, we broke their nighttime feeding in exactly the way your doctor mentioned. Ours said to give them water instead of formula, that made the really angry, so we gave them less formula each night and watered it down. After about 5 nights they STTN.