Duckaholic, your hunting license will cost $85. your Caribou tag will cost you $325.These are last seasons price, don't know if it's going to change,but I doubt it.
To harvest one of these bulls, you would have to be set up on a funnel of somesort on thier migrateion route. Thats the best advice I can give you on arrowing one of these animals.If your serious about pursueing this, start calling game biologilists up here, they are all in from the field. They'd be more than helpful to help you out ,just to get a break from data and analisis. The dnr up here is like no other state.
A bunch of guys on this site that are from the lower 48 have been on caribou hunts and were successful,maybe they would have some good information to offer also. One bit of advice,bring a big bore side arm,bush pilots are 700-1000 $$$ drop float an extra 500. Alot of things to consider. Good Luck, Kevin