Built my own room years ago and one thing for sure, nobody can answer questions like you're asking. Not over the internet. Not without being there. Because there's far more to it than just sound. Its a room, in your existing home, with your existing structure and traffic flow and everything. Best you can do is read and learn all you can about various construction techniques then figure out for yourself what will work in your particular situation.
One thing, I have no idea how you get 2 lines of 110 out of 220. No idea what you found but it doesn't work that way. You either move one wire over to neutral and have one 120V line, or what I would do, get a good quality step down transformer and run 240V in, 120V out to your system. That's what I have and it works great. Wouldn't recommend it if you didn't already have 240 but since you do
https://systems.audiogon.com/systems/8367Next, I hope you bought an exterior solid core door. Because normal inside doors are hollow and crap for sound. Solid core or bust. Also use weather stripping, just as you would an exterior door. This is easily your biggest most cost-effective improvement. Next is windows. You won't believe the noise comes in from windows. Absolutely will not believe. Curtains won't work. What you want are shutters. Will have to take more pics of my system so people can see what I did with the windows. 3/4" MDF shutters close over them most of the time. Stops 90% of the light and sound. Without messing up acoustics like curtains.
Sheetrock, 5/8" costs almost nothing more than 1/2" yet stops sound almost twice as good. Then during construction be super careful to seal around all cracks and crevices especially outlets and light fixtures. The easiest route for sound going either way is holes like around a door, window, or outlet. Those four- door, shutters, sheetrock, gaps- are the end of the really highly cost effective construction techniques. They are just the beginning, but they are so dirt cheap you do them or regret it. Everything else from here costs a whole lot more, to the point you can easily get into six figures just on the room. But you didn't mention a budget so I'm just giving you the stuff anyone can and should do no matter what.