Am I doing this right?

While using a speaker switch will work, there's better ways to accomplish the integration of a stereo system with your theater system. We've done this for many years (and I'm really old :-( ).
Use your McIntosh pre-amp and amplifier to drive your main speakers, no matter what source you listen to.
Connect your sub-woofer using the main speaker terminals, which usually provides better quality sound / integration.
Use an input on the McIntosh pre-amp to feed the analog pre-amp out from your receiver.
This will allow you to use your better quality amplifier independent of what you listen to.

It will also allow your receiver / theater to sound better because it will relieve the receiver of having to power the front main speakers.

The only issue is to confirm your receiver has a configuration which allows the front main signal dedicated to pass out its pre-amp jacks.

I agree with TJ's comments. I suspect, though, that in your diagram you meant to indicate that the speakers are the Aeon, not "Aeos" which apparently never existed, in which case you are in effect already connecting the sub essentially as he recommended.

As far as the failure is concerned, I don't see anything in the setup diagram that **necessarily** would account for it. However, if during some of the occasions when you have been listening to the AVR the MC2205 has been powered up AND has had a music signal provided to it, I would have some concern that that could have been a contributing factor. Although I'm not certain, it seems conceivable to me that since the MC2205 utilizes autoformers at its outputs, running it unloaded (as it would be when the AVR is selected) and while it is processing a signal could cause "inductive kickback" issues. Which are the reason tube amps having output transformers should not be operated unloaded, at least when processing a signal.

Also, I suppose it is possible that when operating the MC2205 unloaded some internal voltages might rise to higher than normal values, increasing the stress on some components.

Also, while I would expect that the Niles switch would be "break before make" (i.e., when its setting is changed it disconnects one amp an instant before connecting the other), if perchance it is "make before break" (either by design or due to some fault) that could conceivably have been a factor, if at times you have changed its setting while the amps were powered up.

The fact that both channels apparently failed simultaneously, though, would seem to suggest that perhaps something else altogether was responsible, such as some age-related internal failure.

Regards,
-- Al