I'll preface this with the fact that I have zero knowledge of the radio in question. I do have Sams CB-23, but that will only go so far.
I'm looking at the schematic and it shows that the tube filaments should be on the same circuit as the panel lamps. If the panel lamps are coming on, are they full intensity? No could mean there's not enough voltage to get the tube filaments to light up. Yes could mean multiple tubes with bad filaments. Multiple tubes all dying at the same time is unlikely, however, if this radio was somebody's parts queen they could have been swapped out over time. Someone with more tube experience will hopefully chime in on whether it's worth it to just do a continuity check on the filaments. I suspect it is and should probably be done out of circuit.
Another thing to look for is bad soldering or a wire put in the wrong place during a previous repair attempt. I'm working strictly from pictures but it appears that this uses point to point wiring and not a circuit board. So putting a wire on the point next to the one you wanted is a little easier to do, especially if you're distracted or in a hurry.
Anyways, that's what I can think of to start looking at. No idea if any of it is actually helpful. Whatever you do, be careful. There may still be high voltage lurking about on tube pins even if the filaments are dark.