Right, I think I've just answered my own question.
Looking at the g-p-m source, it is grabbing XF86XK_Sleep, which is keysym 0x1008FF2F according to X11/XF86keysym.h. Your Fn+F1 is translated to a keysym of 0x1008ff10 (or XF86XK_Standby), which is not what g-p-m is grabbing as the sleep button (or at least I think not).
I think the log you provide will confirm that. The same probably applies to the other keys. I still don't really know which package is responsible though.
Right, I think I've just answered my own question.
Looking at the g-p-m source, it is grabbing XF86XK_Sleep, which is keysym 0x1008FF2F according to X11/XF86keysym.h. Your Fn+F1 is translated to a keysym of 0x1008ff10 (or XF86XK_Standby), which is not what g-p-m is grabbing as the sleep button (or at least I think not).
I think the log you provide will confirm that. The same probably applies to the other keys. I still don't really know which package is responsible though.