How about BOM-BRU-LHR-JFK?

BOM - BRU on 9W in business class, overnight flight in fully-flat bed.
BRU - LHR next morning on BA in economy.
LHR - JFK same morning on AA in economy. Daytime non-stop flight so economy won't be too bad.

BOM-BRU on 9W in business will require 54000 JP miles. You will need to transfer 28000 of CitiPM miles to 9W (2:1 ratio).

BRU-LHR-JFK on BA+AA in economy will require 24000 Avios. Use the rest of your Avios on short hops within US.

AA miles you can keep active by just crediting a flight every 18 months.


OR

BOM-LHR on BA Premium Economy for 32500 Avios. BA fuel surcharges might be ridiculous on its own metal though and you will need to transfer some CitiPM miles to top off Avios.
LHR-JFK on AA economy again using 35000 JP miles.

Let us know what you eventually do !