Well,
If you think the fuel system is good, it's on to electrics.
Since the bike starts & idles, or runs for 5 min or so, And then just dies.
I think I would check all the wiring for chafing, clean & lube the connections w/ dielectric grease .
Make sure all the grounds are clean, corrosion may be killing your bike after it gets too hot to carry the juice...
Remove the kill button and rule that out.
Swap the plug and check the cap and wire. Maybe cut a small piece off each end and re-attach the cap & coil end.
(Ohm out the wire and wiggle it while connected to your meter to look for a possible break.)
That's the easy stuff I think...
Next would be to remove the coil and start checking that.
An ohm meter won't detect a layered short or a breakdown in the insulation or a wire under high voltage, or
that shorts due to heat.
Do you have a multimeter, and have you used one?
set your mmv meter to x1 ohm
between the coil terminals .
primary should be 1.0 ohm +/- 15%
secondary (spark plug lead and ground terminal) 5.9 k ohms +/- 15%
Lets see how all that checks out.
The cdi has a warning not to check it with too high a voltage multimeter or we could damage it....
Tuck\o/