[Arran]

I see to recall reading somewhere, it may have been the A.R.C that the cabinets for these Silvertones were designed by one Edward Coombs, the same man who designed the Philco model 70, 90, and several other cabinets for Philco. Regardless of this fact Sears and Roebuck sold a lot of model 4586 consoles and related models. I don't know much about this particular model but one common failure in many sets is the plate load resistor on the first audio amplifier tube, but I think you checked those. Another fault could be a flaky solder joint on the grid cap/s of one or more tubes, or the solder joint on the grid cap lead. I was going to suggest a failed audio interstage transformer but this  radio doesn't have one, the output transformer would be another one to check but I doubt that would be it since you are getting sound. It could also be a wiring error due to the recap, some of you guys really shouldn't rush this, after you verify that there are no short circuits, power the set up first on a variac then recap it.
Regards
Arran