Glad that you like the sound...
...however, I have no intention of changing the current recording setup with a standard audio cable (and, editing in Audacity) as it costs nothing to do so.
Okay, but please be aware that using the headphone jack for recording is not recommended.
The line out connectors would be preferable, if you wish to stick with the analogue recording method.
Using the built-in recorder involves extra steps in transferring the recording to a USB stick (at extra cost) every time I make a recording.
Recording directly to USB is more efficient than using audio cables, and typically allows higher quality results. Moreover, if you select to record in MP3 format, the file can be uploaded directly to Box.com etc. without needing to copy the file to your computer or additional conversion. Again, a USB stick shouldn't cost more than $5 - if this is genuinely a concern, I would be happy to send you a device.
As for the piece not having any "swing" to it, this is a slow jazz ballad which was not meant to played in that manner. For something with more of a swing feel or rhythm, listen to the other recording of Body and Soul, posted here above.
Yes, I appreciate that the piece is not really supposed to 'swing' in the sense of having a drum and bass accompaniment. I was commenting more on the 'feel' of the playing style.