Why do you need to replace your 2x shifter? Can't you continue to use it? Is there a problem with mixing your old 2x shifter with the new right side shifter?
I thought 3x shifters sometimes don't come with trim? So you'll be losing the ability to trim if you do use it?
I switched my Shimano double FD with 11 speed type long pull to a SRAM yaw FD which doesn't need trim, but continued to use the Shimano long pull shifter with trim. I disabled the trim by setting the high limit screw to high trim which effectively disabled high index position. I can easily get the trigger into high index position. I thought that the extra cable pull and tension against the limit screw simply gets taken up by the spring in the parallelogram mechanics. Or maybe I'm wrong and the extra tension is taken by the mechanics in the shifter?
Anyway because it's a long pull shifter, both the low index and low trim are slack.