Fortunately not too long ago they opened up the Xbox 360 dashboard to support 3rd party USB devices, albeit capped at 16GB, for data transfer.
That means all your saved games can be salvaged so there's no need to run ragged and get John Marston his lasso back. It's not ideal but the complete redesign has the HDD plug into a completely different point on the new Xbox 360 console.
The current HDD models simply won't fit anywhere on the slim design. The trade-off is that the new Xbox 360 does come with built-in 802.11n Wi-Fi which would cost an arm and a leg if you want it for that bulky box from an adaptor.
Does a hellish time of USB stick transfers await you, videogamer?