It turns out I can make my Logitech Rumblepad 2 work with force feedback by using x360ce and selecting the SDL2 input device driver in the RGUI menu. What happens is the SDL driver detects both the emulated Xinput device that’s created by x360ce and the normal DirectInput one so I just have to make sure the emulated Xinput device is set for User 1 in the input settings menu.
I wasn’t succeeding before because I was trying to use x360ce with the Xinput device driver and I don’t think it could differentiate between the two devices (I also tried all sorts of hook / mask options within x360ce to try and prevent RetroArch from detecting the normal DirectInput device). I had removed x360ce before attempting to test the SDL2 input device driver thinking that it wouldn’t be necessary, but it turns out that was the only way it was ever going to work!
As a side note (in case this helps others), Logitech Gaming Software v5.10 needs to be installed for force feedback to function with this controller, newer versions don’t seem to support it any longer.