All good ideas. I still think that the proper adjustment of the carbs can be at fault. I'm not sure about this. Just think you haven't gotten them right yet. And these bikes always run weird after twenty mins if the carbs aren't properly balanced.
Do you have the timing light? You said you would move to checking the timing. That's a good one to get out of the way.
Do /7 tanks have vents? It might say in the manual. Do you have a manual?
I wanted to add my small bit about the cable adjusters. Throttle cables are manufactured to a certain standard so they match and will fit the application they were made for. Those standards are not an exact measure so some inner cables are a little longer or shorter, some outer cables are not exact also. The cable adjusters are here to make up for this little difference found. There should always be some bit of slack in the cables. Don't confuse with slack in the twist grip, that's there also but the cable should not pull the carb throttle while the bike is at idle. Idle is effected and adjust only by the big screw on the bottom of the carb. When you twist your wrist the cables take over and their balance comes into play.
In theory the cables should act at the same time, they should have the exact same amount of free play. In practice this can be hard to see, or achieve. Sometimes one cable will show a definite movement when the throttle is twisted and the other cable will seem just soft.
But check the timing and the tank vent(?) and then you'll be back at carbs again.