alot of fun for 20 minutes at a time

I have a little 1970 Kawasaki G4TR (2-stroke) that I recently rebuilt
and made road worthy and was even able to register and license here in
California-insurance was only $1.00 a year on top of my other bikes!

Anyway, after around 20 minutes the bike will die and will only
restart after cooling down-around 10-15 minutes. Things I have
checked:

-fuel is good - I have clear new fuel lines and it can be seen. The
carb is actually in the case and though I have not checked the float
bowls it should be ok

-vent is not plugged etc

-timing is good but a compromise as I can't set the dwell on this bike

-when it dies I pull the plug immediately and I have spark but it's a
bluish/yellow instead of all blue from cold. The coil tested as "ok"
when I was checking everything out a while back. I have heard
something called "coil saturation".

-the plug looks great almost textbook for a good 2 stroke mixture.

-oh, I am not running a battery in it at the time cause I can't seem
find a little 6volt that will fit it. I do blow bulbs if I rev it too
hard as it's on the magneto. The manual I have says don't run the bike
without a battery but I had lots of 2 stroke dirt bikes that never
needed one.

Well the bikes a blast 20 minutes at a time but I would sure like to
sort this problem

ps anyone know where to source coils and points and stuff as I am at
the point of swapping 'lecy bits.

Thanks
Chris