1. Purchase/borrow the transfer kit/cable, hang on to the HDD, do the transfer once you have the slim, and then bring in the HDD for the remaining credit.
2. Use a USB Flash drive/card reader to transfer your data from the HDD now, and then keep on the drive or your PC until you get the slim, and then transfer back.
You really only need to keep your save data and profile, as you can re-download anything you've purchased by checking your account's download history. But if you've got the room, might as well back up everything you can. And I believe you'll still need to do the "license transfer"' process on xbox.com so any DLC you have will work on the slim offline.
I just remembered that I also have a launch model PSPhat that I don't use anymore. (I use my silver slim all the time) That'll be another $60 in credit toward my upgrade!