Where did you get the "0.5-1%" figure from? That may be true in some cases, but not in this extreme case, here it's closer to half the delta-v (which, due to the rocket equation is enormously less difficult to achieve).
Solar escape velocity is about 16.5km/s* , and since ~99% of this manoeuvre's delta-v budget is used at launch the entire delta-v cost is asymptotically this value.
No, it's about 42 km/s, i.e., sqrt(2) times the Earth's orbital velocity around the Sun, which is 30 km/s. New Horizons was launched to take as much advantage of the Earth's orbital velocity as it could, so that the rocket didn't need to provide all of the 42 km/s of delta-v needed for solar escape.
(You could use the same trick for your scheme, of course. The main issue I see with your scheme is that it greatly lengthens the time that the waste is out in space.)
Solar escape velocity is about 16.5km/s* , and since ~99% of this manoeuvre's delta-v budget is used at launch the entire delta-v cost is asymptotically this value.
*http://en.wikipedia.org/wiki/New_Horizons#Launch (see paragraph 4)