1) I'm glad that you're using a Quad Lock. It is one of four motorcycle phone mounts that I'm aware of that has an optional vibration-dampening option (and I can direct your attention to an Apple warning about this, if you like -- and this may affect Android phones, too, for all I know). The other three are Hondo Garage, Peak Designs, and SP Connect.
2) For mounting, you can go with the Ram 11mm Bolt Head Adapter Ball Base, part # RAM-B-252U:
The RAM-B-252U marine-grade aluminum ball base consists of a 1" rubber ball and 2.25" x 0.875" base with 11mm hole. This part is often used on motorcycles by attaching to the mirror frame. The main brand of bike for the RAM-B-252U is BMW. This part fits well on many handlebar pinchbolts with a...
rammount.com
I went this route on my '22 C 400 GT, with the left bar end. See two pics and captions in my GT gallery, starting with this one:
This is a trivial mod, and I think would meet your requirements.
A second option could be the Ram Torque Small Rail Base, part # RAM-B-408-37-62U:
The RAM® Torque™ small rail base features a B size 1” rubber ball and accommodates rails from 3/8” to 5/8” in diameter. Sizing inserts are included to provide a snug fit and protection of the rail. The mount utilizes nylon-insert lock nuts to prevent loosening in high vibration environments. The...
rammount.com
(The mirror stalk is just under 0.5 inch, so that should work.)
Of course, with either of them, you'll need a double-socket arm. I think the 3" model is the most useful (and shorter than that, they don't include an internal spring).
3) For power, well, that's a more complex deal.
I rode a C 400 X for two weeks in Europe last year, and I used the right cubby for power (for a GoPro). I just sort of mushed the cable coming out of the door, alongside the door, in an area near the top left of the door.
That's not an elegant solution, and I think the doors on the C 400 GT may be a tighter fit. So, you might be able to get away with this, or you might not. Make sure that you have enough cable slack so that it doesn't interfere with the handlebars, if it drapes over them.
A much better solution is to do something like I did with my GT, a couple of weeks after getting it. I installed an external, rainproof, USB port. I did this over on the right (again, for a GoPro), but you can almost as easily put the port over on the left.
I tapped power from the feed to the internal USB ports in the right cubby. You can read the details -- pics, instructions, links -- of how I did this work in my gallery, for a dozen or so images, starting with this one:
This was not a major undertaking, but did involve taking a bunch of the bodywork off and some wiring experience. I think this is the way to go for you, but I don't know how comfortable you are with such work (tupperware removal, wiring, and drilling a hole in a brand new bike, none of which bothered me, as I've done that sort of thing on a lot of bikes).
Edit Addition:
Or, you could use the sat nav power plug, the way I did for my recently added Skene Photon Boosters up front. See this pic/caption/link in my gallery, and the next dozen or so:
You could then run a wire alongside or within the handlebar covers, over to the left mirror stalk. You would then need a USB port that takes 12V input for its power, and has a stalk mount (or something similar) itself.
Or, you could just use your phone on its internal battery, and try to keep it reasonably charged inside of the right cubby, with the stock internal USB ports, when you have some downtime.
I hope you find some of this useful. In any event, good luck. Oh, and yep, I am extremely pleased with how smooth and peppy the GT is, even if it's just a 350cc thumper.