Re: "Rockets fueled by LOX with Hydrogen only generate water"
1) Build a big fracking gun, on par with that German monstrosity from WW2, maybe a little bigger. In fact, make it a railgun, significantly bigger than the ones the US Navy is playing with. That way you can power it off a clean energy source instead of gunpowder.
2) Put CO2 into durable canister rounds.
3) Shoot them into space.
4) Once they're in space, have them captured by a satellite (build specifically for the job, of course) which then fires them out further (via a solar powered rail gun). The moon would make a good target. Or, better yet, shoot it at Mars and we can get a jump start on terraforming it by warming it up a bit. If you don't shoot it out further than Earth orbit then the canisters will eventually fall back into the atmosphere and burn up, releasing the CO2 right where we least want it.
The only problem I see with this plan is that the hardware to make it happen will probably cost more than the GDP of some European nations. If it were build in the US the costs would run into the trillions of dollars.