I think there are some who rent pack goats in Washington and just over the border in Idaho, but I am not completely sure. I remember seeing some posts in the past on the pack goat forum, but not sure where in Washington they are located or if they are still renting. You might want to check out packgoatforum.com and ask the question there.
I never even knew people rented these, I've looked at buying 2 goats. That wouldn't be enough to load out a mature bull in one trip but it'd make the trip in very easy and going out easier. The issue I'd have is finding a place locally to board them since I live in a subdivision I can't keep them at my house. I've heard boarding can run $25-50/month per goat, so you're looking at $600-1200/year, plus the initial cost of $3-500 per goat. After that I figured I might as well pay someone to drop me off and pick me up. I've heard outfitters will pick you up and haul your meat out for about $300, anyone able to confirm this is an average rate? If renting goats is cheaper than the $300ish it'd cost for someone to pack you out then it might be an option worth looking into. Anyone know of any goat rentals is S. Central WY area? Or maybe just put a post in the classified section here for one of you burly guys to help me out for a couple hundred bux if I get something w/my WY gen tag