Oddish challenge with GET variables… halp?

I’m using WordPress for a very unusual application. It’s a kind of “shop” for an RPG where users can select and “buy” attributes and abilities, which are then communicated to the RPG database.

The specific problem I’m having is this: The user gets to the site with a get variable (say “?character_id=g98s70”). It’s the only way to get to the site.

I need a way to have that GET variable available to me no matter how much browsing they do within the site (the site will have no outbound links). That means when they click on categories, tags, permalinks… whatever surfing they do on the site, the get variable has to persist, so when they finally click the “Buy” links within the posts, it can include that get variable in a submission to the main RPG site, which is on a different server.

I should be clear… the ONLY problem I’m needing a solution for is in keeping that variable alive through all the clicks and whatnots, preferably without having to modify the wordpress installation code (hopefully there’s some way I can do it in the theme? javascript? some kind of session marker?)