The Picture control on a 630TS is confusingly named. It is a manual gain control and its effect is not like a contrast control on newer TVs.
The Picture control varies the gain (i.e., amount of amplification) on the overall signal. You may find that it has a pretty narrow range where the picture & sound are acceptable. You may also need to readjust the Picture control when changing to a different source with a weaker or stronger signal.
To some extent, what you're experiencing is normal for a 630TS. At one end of that control's range you'll get almost no signal, and at the other end you'll get wackadoodle picture & sound.
Bear in mind that 1940s TVs were designed to be watched in dim lighting. I suspect we're all guilty from time to time of cranking the controls up too high and expecting these old sets to have an ultra-bright screen like modern TVs, that you can watch in a sunlit room.
There was a recent thread in another forum by a guy who had similar horizontal lines (on a different television) that looked like overdriven video. I think they disappeared when he removed (or changed?) a modification he had installed to minimize retrace lines.
On a general note, if you go treasure hunting to check resistors, check mica caps, too. Micas used to be thought immortal, but now more and more of them are found faulty. When I redid my 630TS 1,000 years ago, an oldtimer told me to replace the mica coupling caps in the video IF chain.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html