I would replace that 6SN7 tube, as it is obviously defective if its output is well below normal and is intermittently shorting. I wouldn't be a bit surprised if that brought your picture back, although I would check every capacitor in the vertical circuit--in a set as old as yours, there are bound to be more than a few defective ones.
BTW, for replacement tubes, I've had good luck with John Kendall's Vintage Electronics:
www.vintage-electronics.com. He has literally thousands of tubes in stock at his warehouse in suburban Baltimore, and they are very reasonably priced. The only thing I would watch is the shipping charges on these tubes. Although the tubes themselves are bargains, the shipping will add another few dollars to the total, depending on where you live. I'm in a small town some 35 miles from Cleveland; the shipping charges to my home for a tube I recently purchased from Vintage Electronics were on the order of, IIRC, $8-$10 or so. The tube itself only cost $2.25. There are other sources for used and NOS (new old stock) tubes as well, some of which may give you a better deal on shipping; Vintage Electronics is just a starting point.