Bottle on frame alternative
First of all: You mention that the placement of the bottle mount is bad. There are adapters which allow you to mount a bottle cage without frame holes. E.g. SKS Anywhere, Minoura or this set. All look rather flimsy though. Mounts for the handlebar or behind the saddle usually look more sturdy, if you have space there.

There is also the Salsa Anything Cage which allows you to mount and tie down anything anywhere.

If a better, more vertical mounting point for your existing bottle cages doesn’t solve the problem, maybe you should get better bottle cages. For example I use these Elite bottle cages with various normal ~800ml bicycle bottles on my cyclocross and I’ve never lost a bottle (except in a 40km/h crash, but that doesn’t really count). They also seem quite popular.