I've had another go at sending SysEx from Cakewalk...

If I create a set of SysEx banks, and then just send them one at a time whilst playing a style on the keyboard - the style changes.

I can tell you that sending two zero style number bytes gets you "Party Polka", if thats any help!

Also, if this technique doesn't work, do you have the ability to set up registration chains that you can skip through by assigning a footpedal to "registration advance"? If so you could use this to change styles using a footswitch, by storing the style in the registration.