I think you are having three issues.
(1) The idea I mentioned about setting up the song's voices on the keyboard, recording a single note, saving it to a USB flash drive as a MIDI song file, and then importing the MIDI song file into your DAW is really just a workaround that some people use if their keyboard doesn't have an "InitSend" or "Initial Setup" function. Since the DGX-660 has an "Initial Setup" function, and you're able to use it successfully (but see #2), that means you don't need to use this workaround; just use the "Initial Setup" function.
(2) It sounds like you're recording one track, then recording a second track, then a third, etc., one track at a time. This is a standard procedure when using a DAW, and isn't a problem. However, the DGX-660 transmits the Main Voice (or Right 1, R1, or whatever the given model of keyboard may call it) on MIDI channel 1, and if I'm not mistaken there is no option to select which channel you want to transmit on. That isn't a problem, either, but it does mean you will need to compensate for it in the DAW. Each MIDI track that you add to your project has track settings which let you set the desired MIDI input port and MIDI input channel-- which most DAWs default to "all MIDI devices" and "all MIDI channels"-- as well as the desired MIDI output port and MIDI output channel. It's okay to use the same MIDI input device and MIDI input channel when recording tracks, as long as you record them one at a time; but you will need to go into the track settings and make sure each track has a different MIDI output channel. Assuming they will all be output to the DGX-660, you will be able to set up, record, and send up to 16 different MIDI tracks this way, outputting them on channel 1, channel 2, channel 3, etc. You will still want to use the "Initial Setup" function on each track-- and when recording, you'll need to arm just the specific track you are recording, so it doesn't overwrite any of the other tracks. Each track will record from channel 1-- but when you play them back they will each go to separate channels, such that their voices will remain separate and as you had set them up to be, rather than the last voice selected being used to play all of the tracks.
(3) The third issue is a question of procedure. As you've seen, recording in MIDI doesn't produce any audio. In order to get audio tracks that you can mix into a final MP3 or other audio file, you will need to record the keyboard's audio output to audio tracks. There are at least three or four different approaches you can take, and you can even mix them together if you like, so I'll briefly describe each one:
(a) You can bypass MIDI completely, recording each track as an audio track rather than as a MIDI track. To do this you will need to use an audio cable to connect your DGX-660 to your computer. One end should be plugged into the PHONES/OUTPUT jack on the back of the DGX-660, and the other end should be plugged into the AUX IN (or similar) jack on the computer. Since the PHONES/OUTPUT jack on the DGX-660 takes a 1/4" or 6.35mm TRS audio plug, but the AUX IN jack on a computer usually takes a 1/8" or 3.5mm TRS audio plug, you can either special-order an audio cable that has a 6.35mm TRS plug on one end and a 3.5mm TRS plug on the other end, or use a cable that has the same size TRS plugs on both ends but use an adapter on one of the ends to convert it to the other size. Another solution is to buy a USB audio interface, which can be pricey although there are inexpensive ones available. You would then connect the DGX-660 to the interface using a standard 1/4" or 6.35mm TRS cable, and connect the interface to the computer using a USB cable. But regardless of the method you use, this will let you play the keyboard and record its audio output to a stereo audio track in the DAW. Then you can record a second stereo audio track, a third track, a fourth, etc., as desired, mix them together to a master track, and export the final mix to an audio file.
(b) You can also continue to record MIDI tracks one at a time. After you've finished editing each MIDI track to correct any mistakes (which is an advantage of using MIDI), and have verified that each track is set up to transmit on a different MIDI channel so it keeps the voice you want, you can connect the DGX-660 to the computer via an audio cable as described above (but also keep the USB-MIDI connection), play back a MIDI track by itself (usually called "solo" in a DAW), and record the keyboard's audio to a new stereo audio track. This is very similar to the first approach described above, but instead of recording the audio as you play the keyboard, you are recording the audio as the MIDI track plays the keyboard. After you have done this with the first MIDI track, you would repeat the process for the second MIDI track, then the third, the fourth, etc., recording the keyboard's audio to new stereo audio tracks each time. You should end up with a separate stereo audio track for each MIDI track. Then you can either delete the MIDI tracks and keep just the audio tracks, or just mute the MIDI tracks but leave them in your project in case you want to go back and edit the MIDI tracks again at a later time.
(c) You can record the MIDI tracks as described above-- but instead of playing them back one by one and recording the keyboard's audio output to several stereo audio tracks, you could instead play them back all at once and record the keyboard's audio output to a single stereo audio track. This has the advantage of being less work and taking less time than the previous approach; but the disadvantage is that you won't have separate audio tracks that you can work on separately before you mix them all down to a master.
(d) A variation of the third approach would be to export all of the recorded MIDI tracks to a MIDI file, save the MIDI file to a USB flash drive, plug the USB flash drive into your keyboard, play back the MIDI file on the keyboard, and record the audio in your DAW as the MIDI file is being played back. This takes a little bit more work than the third approach-- because you have to export your MIDI tracks to a MIDI file and transfer it to the keyboard-- but a possible advantage is that you now have a MIDI file of the song in case you want it.
(e) The last approach is to record each track on the keyboard itself as an audio file, save it to a USB flash drive, import it into your project in your DAW as a new stereo audio track, and repeat the process for each track that you want to include in your project. Then you can edit the audio tracks, apply effects as desired, mix them together to a master track, and export the final mix to an audio file.
You can use which of these approaches, or combination of approaches, is easiest for you to understand or manage-- assuming you aren't required to do it a particular way for a class, such as being required to have a number of separate audio tracks in addition to a final master audio track.
