In the addition of two public keys (or two points on an elliptic curve), modular multiplicative inversion is the heaviest step.
By implementing fast inversion algorithms (such as Montgomery), using coordinate systems that eliminate or minimize inversion (such as projective or Jacobian), or employing batch inversion techniques, the computation speed can be dramatically increased.
Montgomery inversion trick? Old news, at this point everyone's doing it. But it can be further optimized, for a good % speedup. This involves dealing with what the hardware can offer.
Non-affine coordinates? They don't work with either brute-force, BSGS, Kangaroo, or H160. They're only useful in specific scenarios: when adding many points together (for example scalar mul). In 99% of the rest of the time, batched affine with a shared inverse is the fastest option already.
I read about some people trying to use all sorts of other coordinate systems to speed up things. They will hit a wall, after figuring out that it's impossible to make any use of the intermediate results of those calculations, without having to resort to a field inversion
at each step, to get a unique characteristic of any point. So it becomes something that runs slower, since more field operations are used, vs. simply going batched affine.