It could be your previous attempt to hook both the AVR and Int amp to the sub failed (eg the hum) might be because the Exposure doesn't have a true HT Bypass. Meaning its HT input is really a unity gain connection that still passes thru the preamp which would result in the pre-outs being active at the same time as your AVR subwoofer connection.
So the switch approach is probably your best bet.
I have a MF A5 int amp with an HT Direct connection which when selected completely bypasses the preamp section of the A5 so that it only functions as a power amp. Therefore no signal is outputted from the preout L/R connections.
This allows me to hook up my sub to both the AVR subwoofer output and the L/R preouts from the Int Amp. No hum, no switches - works perfectly.
If I'm listening to music, source devices are connected directly the A5 and the AVR is off. The sub gets full range from the A5 preouts and I use the sub xover, phase, and volume.
If I'm watching movies thru the AVR, I select the HT Direct input on the A5, the preamp gets bypasses, no signal from the A5 preouts, and the sub gets the LFE signal from the AVR and its bass management settings.