Trying to get an awards flight into CCU in November/December.

It appears that the only skyteam flight into CCU is on China Eastern through Kunming. There is no direct from Kunming to the US, so it appears that I would have to connect into Kunming.

Questions:

(1) I assume that routing through USA --> Beijing/Shangai --> Kunming --> CCU will not work due to VISA issues.

(2) Would it be valid routing to do JFK-ICN (KE), ICN-KMG-CCU (China Eastern), or JFK-BKK/SIN (DL), BKK/SIN-KMG-CCU (China Eastern)?

What is the best way of trying to find award flight availability on these airlines?