So, I could send it to another address in my wallet and include a decent size fee? That sounds like it could be a winner. It's almost been 2 hours and still waiting for the first confirmation. Maybe I'll wait another hour and then try your suggestion.
There's no guarantee that it'll work. It will only help if there are mining pools that have implemented "child pays for parent" and are looking ahead to see that they can get the fee by confirming both transactions together (it's impossible to confirm the fee paying transaction until/unless the free transaction is confirmed).
Even if the two transactions get confirmed after you send the fee transaction, it's possible that the transaction would have gotten confirmed at that time anyhow. There's no way you'll know.
Best case: A pool that has implemented "child pays for parent" confirms your transaction sooner than it would have confirmed without the second transaction.
Worst case: The first transaction confirms on it's own eventually, and you've wasted the fee by creating the second transaction that didn't help you at all.