Answering my own question here... so, in the end I found a hint in the this threaed: https://forums.presonus.com/viewtopic.php?f=151&t=13964&p=76518 on the Presonus forums. It looks like IK Multimedia plugins don't play with Studio One in the normal way, but there is a really horrible way of getting them working:
For each parameter you want to control:
- Expose the parameter for automation in Amplitube 4, using the "Auto" menu in the bottom right of the plugin display.
- Create a new automation on the track with the plugin, and add the parameter from the Amplitube plugin, it will just be named like "Param 1" or "Param 2".
- Importantly, it seemed like I also needed to set automation to "Write" to make the parameter available to Control Link.
- Tweak the setting, or select it in the Control Link drop down.
- Tweak the fader (or button) on the FP8, or whatever other control surface you're using.
- Assign the control to the Param.
I'm not really sure if there are any issues with having all the automations on the track, but if they're not set to write it shouldn't matter.
Done like this you get the right behaviour with the FP8, and (from memory, I'm not in my "studio") if you rename the parameter automations you get the right names on the scribble strip - I wouldn't swear to that though.
It's better than nothing, I think saving presets with it set up helps so it should only ever need doing once. Back porting it to existing tracks is probably going to be a pain though.
Annoying that it doesn't work out of the box, but so many things with digital recording don't. It's sad, and doesn't have to be that way, but it's up to the companies involved to colloborate more. Probably IKs fault in this case if it's anyone's.