Hello,
The existing controller (Soft Pedel) makes an adjustment to the existing sound, but this may not be enough of a difference to fully recreate the sound you're looking for. You may need to create a new 'patch'? There may be sound banks, maybe some of the more specialised piano sound banks, that have already implemented this.
Might involve a lot of experimentation to get exactly the sort of sound/effect you're looking for.
Maybe try some detailed searching on the web to see what already exists.
Geoff