since you are working in the attic anyway and will need to run a vent etc ... you could also look at an "inline" fan ... that puts the motor (and the noise) in the attic (OOPS >>> THATS WHAT TOM H already Recommended ... x2). ... They can be pretty strong and if you are using gas (or oil) for hot water/or central heating you need to make sure you are not creating a "negative" pressure situation in the house when you run these... again .. would ask the HVAC specialist in the family
... incidentally if you went with TomH suggestion you may be able to pull the motor/fan assembly out of the existing unit and plumb right into the exhaust pipe we can see in the attic shot with an insulated hose (or metal duct if you prefer) and install the inline fan from there.. just a thought
... BTW
if that insulation is vermiculite it could/"MAY" contain asbestos ... if so:
a) dont disturb it when you are up there... and take precautions
b) dont run the existing fan till you exhaust the fan to the outside
c) make sure there are no other penetrations into the ceiling that could spread the dust
(I can think of another several don'ts but common sense will dictate ... "IF" it is vermiculite and "IF" it contains asbestos ... could also be why the inspector didnt spend a lot of time poking around in your attic)
see this link..
http://www.hc-sc.gc.ca/hl-vs/iyh-vsv/prod/insulation-isolant-eng.php
Incidentally .. I assume you are in Washington State ... are there any regulations regarding home sales and mandatory declarations about asbestos etc? I would see if there are any old scraps of paper left up there that say "Zonolite"
(will add ... I see an old box peaking out of the insulation ... wonder whether the original electrician was on the ball ... and a DIY'er later decided to forego the "formalities" when they put the fan in.... did they replaced the original ceiling light with a fan/light combo - and didnt know WTF they were doing??)