Not imposible at all! Like I said, make soem friends. I know there are a lot of guys that come up every year throught the hunter host system.
Your worried about an outfitter and paying for it but that is exactly what the most part of hunting in the U.S is isn't it? Pay for access, pay for landowner tags. I have a buddy in Utah who spent $20K hunting his elk 2 years in a row! He said even if he drew a tag he would still have to pay thousand of dollars just to access the land he wanted to hunt.
There are definately more opportunities available to those with $$$, but most elk shot in the US do not cost thousands.