You can ask for enough meat to fill a standard top of the fridge freezer. I forgot how much cubic feet that is.
Some farmers will sell you a 1/4 or 1/2 and they take care of finding someone to sell the rest to.
I'm also afraid of freezer burn. I think the best you could do would be to ask family and friends if they'd like to do this (you could even split by 6-8 households if no one has a freezer). You guys set a date (say, mid-January?) and people can work on emptying their freezers so they'll have room.
Since you are in Seattle, I imagine you could easily ask if someone in Craigslist wants to share a cow.