How about building huge ring like slingshot/accelerator devices and plant them along the route to Proxima Centauri, you'd set off in a space craft as fast as you could by slingshotting yourself around Jupiter or whatever and you'd cruise at huge velocity towards the next star system and enroute you'd pass through these slingshot devices that accelerate your craft even faster until eventually you're travelling at super speed and you get to proxima centauri much more quickly.
a) How do you get the 'slingshots' out there in the first place?
b) The 'slingshot around planets' technique works because planets are very heavy compared with the probes looping round them, which steal a tiny tiny fraction of the planet's momentum in the pass. The slingshot devices would have to be of planetary mass to be of any use. Which leads back to a)...