I had a cow moose tag back in 2008 on the East Canyon unit and all I could find were bulls...and yes most of them were small. I hunted all or parts of 15 days throughout the season and saw exactly one bull that I would consider a "good" bull. He was probably high 30s, maybe low 40s wide with good palms and 8-9 points per side. I saw him in mid-to-late Oct. after having hunted on and off since mid-Sept. The moose herd has dropped off quite a bit since then, but I still think the overall pattern applies. You will see lots of younger bulls, but the bigger ones will take some time and patience.
I'm scouting a small patch of public land this weekend for the upcoming general elk hunt and it's right inside the borders of your hunt unit. If I see anything, I will let you know. I've never seen anything big in this particular area, but you never know.