Jeff,
You want to pull the HO tube out because it would end up running too hot. Since you are only giving the set partial power, the horz osc tube won't be reach the correct frequency to drive the output tube. The plate of the output tube will get hot enough to glow... not good.
You only want the HO tube in there once you can give the chassis the full line voltage.
Black beauty and paper/wax caps are always prone to failure. It's best to simply get them out of there. I've been changing alot of BB caps in my Zenith, and in doing so, I've corrected a lot of problems. Many of the BB's i've changed actually checked good out of the set... but in the set and under a load, they simply couldn't hack it.
In any case, they're 50 years old and need to go.