Hi John,
You probably have "Songbook+" (SB+) on your iPad (not "Songbook Pro"). Basically, you can only link Registrations with PDFs in SB+, not the Styles directly. So you would have to create at least one registration for each style (and then of course save the Registration Bank as a file). Normally you use a separate Reg Bank for each song you want to play.
After you have loaded the desired Reg Bank and activated the first registration (Reg button #1) in it, you link this state in SB+ with the desired PDF. The link then works automatically in both directions. By the way, it is important that SysEx Transmit and Receive is switched on on the keyboard. Therefore, make sure that the Preset MIDI template "All Parts" is activated in "Menu > MIDI".
P.S.
You don't have to copy the styles to the SX700's User drive, you can leave them on the USB stick. But you must not move or rename the styles on the USB stick (not even the folder in which the styles are located) later after you have included (linked) them in your registrations.
Hope this helps!
Best regards,
Chris