Today I re-installed the front plate as well as all the knobs, excluding the two broken ones. My JB Weld experiment did not work out well as the knobs almost immediately came apart again, I suspect I added too much of one part to the mixture. Will try again at some point, but it's not crucial as the shafts are still very accessible from the front.
I've been fiddling with the AGC and buzz controls and was able to reduce the buzz quite a bit, but the audio is still too quiet. I'm starting to suspect the audio tube is weak.
I might make another post if and when I figure out the audio problem, but for now I consider this project pretty much finished. Thank you to everyone in this thread who helped out with the set's various problems, your advice has been invaluable to me.