Are you using this Hori with your HAS?
How is it connected? Are you using it for any other systems? (Do you need it for any other systems?).
CPS1,2,& 3 down't need their own individual presets. Aside from fighting games, most just use up to 3 action buttons that number left to right. ('Preset 1' if you down want to reach over other buttons).
Presets 1&2 are suggested mainly to work around the fact that Capcom fighting games place Punches on the top row and Kicks on the bottom row.
Most 6 button controllers have B1-3 on the bottom row and B4-6 on the top row which is upside down for those fighting games.
'Preset 3' gives a usable option for 4 buttons on the same 6 button layout.
If you have 8 buttons to play with you can wire things differently, but then i would suggest you mod your Hori stick for DB-15 and connect buttons as you like.
I have modded an 8 button stick similar to yours into a 7 button layout with a hard wired switch to alter layout like so:
1 2 3 4
4 5 6
4 5 6 4
1 2 3
The 3 button games you mention again don't need their own individual presets as they will work fine on 'Preset 1'