To answer your question about the mule, YES!
I know the issues well; Coggins test, livestock inspection certificate, slower travel, water and feed 2Xs a day = getting up earlier and staying up later after you're worn out.
But with my limited experience (archery elk, new early elk and 3rd season deer) I'd say yes.
I would imagine the better bulls would be pushed away from pressure after a month long archery hunt, 9 day muzzy hunt and 2 previous rifle hunts.
There are a lot of areas in 61 you can easily hike to and be 1-2 miles from a road and be into bulls. But some of that country is pretty steep. After waiting 23 years for the tag, I wouldn't want to have to think how I'm gonna get him out. Or not hunt an area for that reason.
Just my 2 cents.