You could have a cathode to G1 short on the green gun. You could have
super low emmisions on the red and blue and turning up the screen voltage
high enough causes the green to go way high.

I am betting on the picture tube being bad, from lots of Zenith experience.
They tend to go green.

Yes, the next step is to swap the drive between the green and red guns
right at the crt socket pins.

Do not forget to remove and check the ~150K ohm resistors on the crt board
as they often open/change values messing up the crt color.

As well you should make sure the RGB drive controls are all set midrange to
be sure the voltages to the tube are all close during testing. You will
have to reset gray scale when you have completed the repair at this point
no matter what happens due to the age of the tube.

David