Agreed, do not run the bike until you get this fixed.
When you fill the radiator as you mentioned, how quickly is it emptying? How much fluid are you putting back in?
The white smoke does make it sound like it is the gasket leaking into the cylinders, however, it's possible that that two are unrelated. Is it smoking from both mufflers, or just one?
In the event that the leek is not the gaskets, you will need to find the source of the leak. check around the outside of the engine looking for any drips. Check the hoses to make sure they are securely clamped in place and not cracked and leaking. If it is a gasket issue and it is leaking into the crank case, then there is a fair chance that the coolant is getting into the oil. I would recommend draining the oil to see what it looks like.
If it is a gasket that needs changing, this will be a decent amount of work. You will need to completely remove the engine from the frame to get the head off, whether it be one or both that you need to do.
This will of course then involve having to time the engine/cams once you put the head back on.
......I'd rather wake up in the middle of nowhere then in any city on earth.
*2014 VN900 Custom (16,200 miles and counting)