I agree that Luang Prabang and Siem Reap deserve a bit more time. I'd do it by cutting out Chiang Mai, thereby eliminating a stop and giving you more time for other destinations. (as many here know, I'm not a fan of CM)

Lucky to go on such a great trip. You only need a day for agra. I would not want to be there for longer than that. Also I would avoid Phuket. It is pretty much hell in paradise but is a hopping point for some of the smaller islands. If you like beaches I would check out the Anadaman islands in India which are amazing and more secluded.Have you thought about Borneo? In my opinion Calcutta (kolkotta) has much more to offer than Mumbai but many people may disagree. Mumbai is a pretty big commercial city without much to see. You may want to check out a hill station like darjeeling or manali. Are you interested in seeing just big cities? I realize that big cities are the most easily accessible but you may miss out on some amazing opportunities in some of the countries you are visiting. Whatever you do this trip will be amazing. I just hope you realize the distance between all of these places. I like to see a lot but you really are rushing a lot in. This trip takes many people 1 year or more to do.