Like Fred, I also thought that this was not possible, however looking at the Reference Manuals and Data Lists of the '609 and '709, it appears that as well as in registrations, the functions assigned to the Centre and Left internal pedal on certain CVPs are stored as part of the Voice Edit (Common) parameters (Voice Set).
This is what the CVP709 Reference manual says about this on page 45 in the section: 'Editable Parameters in the Voice Edit display'
Pedal
This section allows you to select the function to be assigned to the center or left pedal. Before making any settings, make sure that the current part is set to Main; in other words, you should select the Main part by touching the Voice name at the top of the Voice Edit display, or by pressing the VOICE [MAIN/LAYER/LEFT] button. The settings here are called up automatically simply by selecting the corresponding Voice.
This presumably means that if a voice that includes pedal assignments is loaded into the MAIN voice part by any means, including a style (with OTS), MIDI song, or Music Finder, the left and centre built-in pedals could be set to different functions.
Although the OP seems to be saying that all three pedals are changed with the voice, the manuals suggest that only the left and centre ones are, with the right one remaining as currently set.
I spotted the following on page 38 of the 709 Ref. manual which may help:
4 If you change the functions of the Center and Left pedals from the default settings, turn
“Switch With Main Voice(Center & Left)” on or off as desired.
When this is set to off, the function assignments of the Center and Left pedals are maintained even if the Main Voice
is changed (page 45).
If the above does not do what you want, I would agree with Tom G. that it is worth trying the Freeze button after checking the 'Pedal' group in the Freeze table. This works with certain parameters on my Tyros4, even when not using registrations.
Regards
Ian