Jason, I'm glad you made it here!
As I mentioned on the other forum site, I don't have a PSR-S970 or similar model.
From what the manuals say, it sounds like you're supposed to be able to select DSP1, set its "Connection" parameter to "System," and then the chosen DSP1 Effect Type will be applied to the entire system-- in this case, all 16 Channels of the Song. Then you can set the Send Level (Depth) of each Channel, and Return Level for all Channels.
If you wish to use different DSP Effect Types with each Channel, then for DSP1 you must set its "Connection" parameter to "Insertion." I think for DSP2, DSP3, and DSP4 they are always Insertion? The manual seems to say that you can then select a different Effect Type for each Channel, but I don't see a step-by-step guide on how to do that.
EDIT: Unfortunately, I don't see any illustrations that show that "Connection" parameter they mention, nor do I have any way to try any of this myself; but there are several PSR-S970 owners here, so hopefully they can help you work everything out.