Here's how you can (probably) speed up getting this nonstandard transaction confirmed and making a payment to 1EG... of 0.054... btc.
It's a little technical and will require you to use the Satoshi client's debug console.
1. Create a raw transaction spending the change output from your unconfirmed transaction to the address you want plus the rest of your btc in change back to yourself. (DO NOT FORGET THE CHANGE OUTPUT OR YOU WILL LOSE YOUR BTC.) You should also include an unusually large fee to encourage a miner to take confirm both it and the previous transaction. Here's a partial version with roughly 1.7 mbits as a fee. (It's "partial" because I can't read the full 1EG... address.)
createrawtransaction '[{"txid":"b96f736e798fa221b316ee73ef5a2401a12fdf2a7cd40068fd3f6633df1c9acd","vout":1}]' '{"1EG...":0.05446166,"1P7gsbyDeKTgwrpEC5TduNRGbZV5abuv5D":2.446}'
2. Sign the transaction with the private key for 1P7...
signrawtransaction
3. Send the raw transaction to the network.
sendrawtransaction
I hope this helps. There may be other tools for doing this than the Satoshi client. I'm only telling you the way I'm familiar with. If you have any questions I should be online for another hour or so.
I've done this kind of thing before...but...
Disclaimer: This post is for informational purposes only. I am not responsible if anything goes wrong.