I've never actually glued one of those coils back together before, but I figure wood glue will work well on that material without harming it.
I'm just about done down in this cramped corner. The original 0.005 mfd cap across the audio output transformer had been replaced with a 0.01 mfd.
I put it back to 0.005 mfd but didn't have any more nice yellow Aerovox caps to restuff.