You're in NYC, right? I'd call the guys at Dior Homme (Hojo, in particular), as they have some special cleaner whom they recommend, literally, there is only one in the city who gets it.
I'm in Suburban Philadelphia and spend extra money to get all my dress shirts cleaned as "tuxedos" and "hand pressed," which has worked thus far with only one or two minor tragedies in the past four or five years. I consider it a cost of doing business. I don't wear suits and outerwear enough (or go into smoking environments) where I need a cleaning for them.