That Zenith TV looks great--good picture for a set from the late '50s or '60s. I've had several vintage Zenith TVs (two of which had a light-through projection channel knob like yours), but never one exactly like your SC300. I did have an SC300 portable Zenith in the late 1970s, but I never knew if the remote control worked since the hand unit was missing, as was the motor drive for the VHF tuner.
I had to get rid of that set because the horizontal output tube went gassy and I couldn't find a replacement. I think the HO tube was gassy because one day I turned the set on, only to find the picture badly washed out on all three VHF channels in my area. This set uses keyed AGC, which depends on proper operation of the horizontal oscillator-output stages for its own correct operation, so when the HO tube became gassy it threw the whole thing out of whack. My set used, IIRC, an oddball (almost unobtanium by the late '70s) HO tube with a 22-volt filament; the local TV-electronics parts store didn't have it. Hated to do it, but I junked the set and bought a 12-inch Zenith b&w solid-state portable the next day.
The strange thing was, the Zenith SC300 lasted me all of one year before the HO tube went bad, while the new solid-state portable which replaced it lasted 22 years and was still working when I moved in 1999. I hated to get rid of it, but I had moved to a small apartment late that year and had no room for the small set; I already had two color sets (a 1995 Zenith SMS1917SG 19" color table model and a new [at the time] RCA CTC185), and the apartment is very small, so unfortunately, the 12-incher had to go.
I hope whomever picked it up from behind the apartment building where I live got a few more years of use out of it, as the set was still working quite well and the CRT was still very strong. Being a Zenith, I'll bet it did work for a few more years and may sitill be working today. Those sets were built to last, unlike today's BPC/SPC throwaways.
Good luck with your "new" (to you) Zenith TV.