Definitely do not rejuvenate the CRT at this point. Too easy to kill the tube, and what you're seeing on the screen may be normal for a CTC-4 that's chock full of bad caps. A working television will tell you more about a CRT's condition than any tester.
I agree with old_coot88, that pop sound could be arcing, and the cutout in the CRT metal retaining ring is an obvious place to look. If you run the TV briefly in a completely dark room, you might even see the zap occur along that dark track seen in the photo.
When I installed a glass CRT in my set, I made a smaller cutout in the ring, but I also covered the nearby edges with cambric insulating tape rated for 90KV. More about all that in:
http://antiqueradio.org/RCACTC-4ColorTelevision.htm
You are right to think of this as a long term project. Be patient and it will all get done. CTC-4s don't come along very often, so enjoy working with this one while you can.
Have fun!
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html
P.S. What's in the little metal project box? Looks like a relay and a tube on top . . . ?