Could a low/high pass filtering solution work, or are the higher harmonics of the low notes too important?
It can have an interesting effect - in fact I have experimented a lot with this on bass guitar - but you are correct that the harmonics of the lower notes would be above the fundamentals of the higher notes, and so you wouldn't really get full separation of notes. Even with very low or high notes, parts of the 'noisy' initial transients will appear on both sides of the crossover filter output.
On the plus side, this technique should be easy to experiment with using a conventionally-recorded part. You can simply clone your track and pass differently-filtered versions of it through different effects. You might even be able to chop-up copies of the track in the time dimension too, to create a poor man's version of Todd Wilcox's suggestion.
One way you might get even more separation could be to load your recording into melodyne and see if you could use that to separate things out. You might even be able to achieve some effects that can't be achieved by treating things per string - e.g. you might be able to isolate runs and riffs that go across strings.
or using a custom guitar with two sets of pickups, which would be way too much effort.
This is likely to be a much more inspiring playing experience, IMO. You don't necessarily need two sets of pickups - If you google for hexaphonic pickups, polyphonic pickups, or divided pickups, you may find something that would fit in an existing guitar with only a rewiring job needed.