I often ask myself, is it possible that there's nothing wrong with the bike. Yep, the battery is sad, the Voltage is sad but it might be much worse in the Amps department. You want to get it tested, or if you can get hold of a good one, just as a test, give it a try.
It would probably be good to video the instrument cluster so you have time to look at the many clues which might show up when it goes into idle mode. Like check if the choke light, clock, and backlights work, and if they also work in stuck idle mode. No choke light might point to a power problem, only two backlights working might point to an earth problem. No clock, probably a power problem closer to the battery, or the battery. They're just a couple of quick checks.
I like the suggestion by Laitch about the possibility of bad coils, especially if yours is the earlier version where the grab handles are incorporated with the seat. I have one of those models, both coils failed the tests suggested by Laitch, they both also had cracks on their cases which were easy to see.