The good news is that the B side voltages look good.
The fact that the LEDs are not lit on the A side of the shunt reg board indicates it is not functioning. On page 58 of the manual (at least the version I have) are instructions for checking the shunt reg circuit. Do those tests (you will have to backtrack to identify the connections). While you are there, measure the voltages at the A side of the board - OA, IA, kreg, -, +reg , breg , bA. From this we can try to figure out what is wrong with the regulator, hopefully without further disassembly! While you are at it, try to see if both heaters are lit on the shunt regulator tube.
Be careful and patient here! This is the high voltage supply. Use clip leads, no hands while the circuit is hot, and let it sit after turning it off for enough time that the voltage drops, as described on page 58.