Gorilla Cage is the big one, for sleeping bags and stuff. Monkii Cage is what you want.
The normal one just slides on, thobut. I have vague recollections of an alternative slide-and-twist version for fitting in small frames that might be a bit more pavé-proof.
Regardless, you'll need to beef up the single velcro strap securing the bottle.
The Gorilla Cage would probably be more suitable for a 1 litre bottle, giving support higher up, having 3 straps attaching to the back plate and also a fabric-based retainer at the bottom rather than the perhaps more risky plastic shelf of the Monkii. It doesn't have plastic wings either, so can be matched to the diameter of what you're carrying, hook and loop section coordination permitting.
It also comes with a separate velcro strap with silicone grippy strips on the back for wrapping around the bag and the relevant part of the fork or frame. Might one of these fancy voile straps the cool kids are talking about be deployed to similar effect?
The mount Kim is thinking about is the V-Cage. That really only affects the interface between cage and mounts though, although might be useful on pavé. The Gorilla Cage mount has a similar action.
[slightly cross posted with Cudzoziemiec]
Seth Bike Hacks has done a video on bottle cages for techy mountain biking. That might be of use to you.
https://www.youtube.com/watch?v=Gxw6L0QmPF4I think he also uses a magnetic set up. Maybe the Fidlock bottle? (Gets a bit of a battering here:
https://youtu.be/UADXI9BJRs8?t=181) I don't know if there are options for larger bottles though.