Personally I’d prefer the bottle on the TT but nadger clearance is always worth having too I suppose.
If you have to put it under the DT then something like the ‘Elite Fly’ with a cover would make sense as it’s going to be in the front wheels spray path.
As for mounting the cage, it’s only an experiment, you could pay over the odds a for a 3D printed mount or just buy some sturdy zip ties and put a bit of neoprene/foam/cut up old innertube underneath to protect the paint.
Just pick a cage that lends itself to being zip-tied on, and use three for a wee bit more security.
I like Blackburn Al cages, as you can bend them a bit tighter to reduce the risk of bottle ejection…
Have fun…