Well here's an update - it doesn't work. Not in the intended way, anyway.
In order to be able to use both a SteamVR headset such as Index and an Oculus one on the same PC with a single sim installation I have to reinstall whichever one I want to use.
So, say today I use my Index - the Steam/Vive version needs to be installed - goes without saying. Next day I want to use Quest (with Link), so I have to install the Oculus version of Fly Inside. However, I don't need to reactivate it - the single activation is valid for both versions, as long as I don't actually uninstall FlyInside, the activation is good.
Next day I want to use Index again - but I can't use it, because whichever version was last installed overwrites the config - so FI will try and start whichever code was last installed - Steam or Oculus. As I had used my Quest yesterday, I now have to reinstall the Steam/Vive version to use my Index today.
It sounds more hassle than it is. Though I was disappointed about not being able to have both on the go at once, it makes sense this way. Just run the installer before starting the sim and you're fine. The config remains unmolested, so your assigned buttons and set-up for FlyInside are constant and as mentioned, no reactivation necessary.
So it works well enough