Just the thicker or oversized disconnector will remove the pre-travel in SA and the slop in the trigger on reset. The reach reduction kit does not have an oversized connector so that will not be a problem.
Your connector needs to be fitted to the individual gun to work correctly. It only takes a few thousands to make it work or not work. Every pistol is its own book so you would need it fitted to your particular gun for it to work correctly. I would do that for you for free if you want it to work correctly. I don't charge anyone on this forum for work except for the freight and transfer fees. PM me if you would like to get that done.