Once you've created User Songs that way, you should be able to save them as SMFs or MIDI song files, load them into a MIDI editor on your computer, and remove the single note that was required for making the recording on the keyboard. That should leave just the messages which select the voices for the various channels, and you can save the modified file as though it were a song even though there are no Note events in it.
When you're browsing through the available songs on your keyboard, you don't even need to press Play or Start, because as soon as you browse to a song file in the list the keyboard will load the indicated voices in preparation for playing the song. This is similar to the way that more advanced PSR-S, Tyros, and Genos models let you create User Voice files, which are simple noteless MIDI files that select an available voice and then apply changes to it as programmed by the user-- that is, adjustments to the volume, pan, reverb and other effects depths, and even the ADSR envelope and filter settings. But on those models these files have special filename extensions such as .VCE (for "Voice"), or .LIV (for "Live!"). The DGX models aren't programmed to recognize those extensions, but those files are nothing more than .MID files without any Note events in them.
If you plan ahead, you can create "song" files like this and name them in such a way that they'll be listed in a given order-- that is, alphabetically and numerically-- so if you plan to play a particular song and you'll need to switch voices five different times while playing that song then you could name the files something like MySong01, MySong02, MySong03, MySong04, and MySong05. That way you can navigate to MySong01 and begin playing, then advance to MySong02 at the appropriate moment, then advance to MySong03, etc.
If you make the initial "song" recordings on the keyboard, you'll be stuck with the settings (Volume, Pan, Attack, Release, Cutoff, Resonance, etc.) which are defined for the preset voices, unless you adjust them in the Function menu while setting up the song-- except the DGX doesn't have functions for Attack Time, Release Time, Filter Cutoff, and Filter Resonance as the PSR-E463 and similar models do. But once you load the "song" into a DAW or other MIDI editor, you can adjust those "hidden" settings and have a lot of fun creating "new" voices-- not really new voices, because they still use the built-in voices, but adjusting the Attack/Release and Cutoff/Resonance can make them sound totally different.
Also, in a DAW you can set up voices for all 16 MIDI song channels if you want, and depending on the features in your DAW you should be able to layer or split those 16 voices as you wish, such as layering three or more voices together instead of just two, or splitting the keyboard into three or more voices instead of just two, or layering two or more voices together on the left side of a split instead of being limited to just one voice on the left, etc. This is sometimes called "MIDI effects" in some DAWs, and you can filter the Note events of a given MIDI IN channel by their Note values, then redirect the filtered Note events to a given MIDI OUT channel.
Another possibility would be to play some of the channels live, and use the voices on the remaining channels for Notes which are being sent to the keyboard by your DAW or other sequencer.
But you have to be careful when doing these sorts of multi-layers, multi-splits, and sequenced channels, because it will eat away at your keyboard's maximum polyphony. I believe the DGX-660 has a nice, high maximum polyphony, so you should be okay as long as you don't start using the sustain pedal. But my PSR-E models have maximum polyphonies of just 32 or 48 notes, so I have to be very mindful of that!
