I have no experience with double towing (not sure I ever would want to), but I do know, anything you can do to improve the safety of your rig is well worth all the effort and expense. Adding the sway control will not hurt anything. I don't know how well it will improve anything, but it definitely will not hurt anything.
Regarding your trailer weights, I'm clueless there. No advise to offer, except, I wouldn't do it if it were me.
Who you are right now is a sum total off all you use to be.
2019 Montana High Country 375FL
2014 Chevy Silverado Duramax, 6.6L Dually