that sucks man, i'd do it but i'll be in wisconsin.
no hotel shuttle/bus? maybe call them, i'm sure they have advice for the best way to do this.
have you called the shuttle companies? there are a few there that do like a ride-share thing and i've heard if you call ahead and there are a few people on there it is cheaper than a cab but it may take a bit longer because they have to go to all the different stops.
if you really wanted to you could probably take a cab to the closest trax station (which would be near downtown) and take that to the closest stop to your hotel, but that would be HUGE pain in the ass with gear and luggage and probably worth just paying for the cab.
in a few years they'll have trax running from the airport, which will make things soooooo much easier.