Greg Egan's story "Riding the Crocodile" features a fancier version of this trick, fire three objects from three origins at close to maximum speed, precisely timed to arrive at a point despite the enormous relativistic delays, the objects incorporate powerful magnets, and are designed such that they don't actually collide per se if timing is correct - but as they pass each other at the point where they would collide if shaped differently the magnetic force slows them all and so they eventually stop, together, at this focal point.
The Amalgam in that story have fantastically better technology than we do, but this is certainly at the edge of what's practical for them. It's a fun idea though, I wonder how close we could get with our technology.