Shiras moose tags across the west are tough to come by for both resident and non-residents. even cow tags. in fact many units only have bull tags and few of them. You will have to put in some time researching your draw odds and areas for what kind of hunt you are looking for. In a number of places in WY for example, it takes around 15 points to get drawn.
Good luck in your moose endeavor! I hope to draw a tag some day, but will just begin building points this year
"If you are going to go through all the trouble to put a hole in something, why not make it a big one?"