Personally I would not suspect or have concern with D805 and D806. I mean, you can test them, but this is a relatively low voltage low current circuit, and all those diodes do is ensure proper current flow at power up and power down in order for the transistor “on” state to be delayed at power up, and go “off” first at power down. We know, based on your tests, the transistor Q801 is bad. It may have simply failed from age, and went dead-short emitter to ground. Current if I understand the circuit correctly current is t supposed to pass to ground through Q801…the emitter is a reference to ground so the transistor knows when to go “on” depending on the voltage level at the base. But if it failed and current went to ground through Q801 when it failed, I think that would pop the fuse…and after failing Q801 might be open circuit to ground which is why it’s not blowing the fuse, but also not passing enough current to the collector to energize the muting relay coils. You could always test this and clip the emitter pin and jumper the base to the collector, turn it on and see if you have audio…beware you will likely get a power thump in the outputs at power up, so turn down the volume level of your monitoring system. I realize you’ve got it all pulled apart now and that can be scary trying to ensure nothing is touching anything it shouldn’t be touching. I’m sorry I didn’t think of this earlier, but it is something you could do to verify the rest of the circuit is working…verify the transistor is the culprit.
If you do this, again, make sure you allow adequate time for the large caps on the power supply PCB to drain before working on anything.
Regarding the rabbit hole, if it was me, I’d probably recap the power supply while you have it out. If you do this, at minimum, use 105C temp rated caps.