If I understand you right, you only need the 10 metioned sounds ? Maybe you give the browse mode a try. RTM: load rig -> press SYSEM -> Browse Mode PrgChg -> MIDI PrgChg# and assign the midi-number. (In performance-mode the numbers are fix: (#performance-1)*5 + (#Slot-1) )
AFIR the 0-button on the z-12 sends "1" and so on.
I own a Z12 but as I play in a coverband making use of many sounds, I bought the remote...
BTW: the Z12 doesnt brake !
But if something else is not working, you can name the 10 rigs in alphabetical order, make them favorites, and mask the other rigs. So I case somethng other brakes you change the rigs directly at the toaster.
Hope this helps.