Hunter09
I hunted Shiras Moose in Wyoming many years ago, back when moose were much more plentiful than they are now. The best advice I got back then was to be cover as much country as possible and talk to as many people as you can, who know the area.
I'd start with the DWR biologist over that area and then go from there. You've already got an offer from a fellow MMer above so stay in touch with him for sure. I'd recommend talking to anyone you meet who's headed to or been in the area and ask them if they've seen moose. Most people are happy to share their encounters with a Bullwinkle.
Moose are not hard to spot in the open, but they are big and black and they don't like the sun on them when it's hot, so they spend a good deal of time in shady timber. So don't give up easily on a spot that has moose sign.
If you can find some areas where some cows are hanging, when the rut comes on there will be a bull or two around, so keep checking on them.
You have a rare tag indeed, so I wish you the best. Have a blast.