I've been meaning to pick up the left shifter regardless of whether the GX would work.
Even though I'm in the states and had to pay shipping, that planet x discount saved me probably $20 over the cheapest new left shifter I've found over here. Next, cassette.
Yes, that will work. Have run gx rear mech with sram 2x11 and 46/30 x 11-40t
The left hand shifters are still super cheap on Planet X fyi