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Six weeks is a nice amount of time to play with. To avoid costly zigzagging, I suggest you do a generally circular route, ending up not in Beijing but in Shanghai, from which you can also get a flight to India. I suggest for logistics and for weather purposes, you go:
--Hong Kong and Macau (4 days)
--Guilin--Yangshuo region and Rice Terraces (5 days)
--Yunnan using Kunming as your gateway: Sample selection: Lijiang, Shaxi, Dali, Shangri-La maybe beyond (10 days)
--fly Shangri-La to Chengdu, Chengdu area (3 days).
--Skip the Yangtze Cruise.
--Chengdu to Xi'an by flight or overnight train
--Xi'an (2 days)
--Xi'an to Beijing travel including Pingyao, Datong (4 days w/travel)
--Beijing (5 days)
--bullet train to Nanjing (2 days)
--Suzhou, water town, Hangzhou, Huangshan (some combination, allot 6 days incl travel)
--Shanghai (2 days)

This is just a rough pass which you need to hone from more research and apply your own priorities. Even with 6 weeks, you'll have to be selective. For instance, you may wish to forego the Pingyao/Datong route and put more time in Sichuan such as Emei Shan and Leshan. Or Lugu Lake in Yunnan which then positions you for an overland exit into Sichuan.