I've been gone for several months and would really like to start the campaign over again, especially since I've done a pretty terrible job building decks and characters. Is this possible without having to create a brand new account?
You can create a brand new party if you want, characters are recruitable from the Inns. However, there's no way to reset progress, loot (unless you sell it all and pretend the gold isn't there) or the dialogue popups without the intervention of the devs. If you bought any pizza on your account, or don't want to start over fresh on another account you can always try sending a request with your account name - and reason for the request to support@cardhunter.com.
You can always create a new account or play on the test server, but then nothing transfers to your main account. Or do what they call a "nudie run challenge", where you start out unequipped, then do one mission of each level, and only put items in and out of the treasure chest (not using club rewards).