Online reviews of the brake don't rate the original pad highly either, so I think I'm on the right track.
The existing set up is shown below. It's a 50mm pad, with a threaded shaft and a domed nut.

I'm having a heck of a time understanding all the pad options on the market and their compatibility with different brands/systems. Seriously, how hard is it to have a pad that fits a slotted caliper arm and attaches with a nut or screw? Will anything do, or should I look for compatibility with any particular system? (or equally, avoid any particular compatibility?)
I think the only limiting factor may be not going for too long a pad due to the small wheel radius. But whatever is the grippiest compound available would be best, and given the use I have zero concerns about wear rate or heat capacity.
Thoughts and help appreciated.