FYI, there are lots of papers on parallel shortest path algorithms. If an approximate solution suffices, there’s also a lot of research available on that, often with some parameter that lets you trade more computation for a tighter approximation. It's not a problem that parallelises particularly well though, so not sure if you'll see good gains in practice.

If you can restrict the structure of your graphs (e.g. planar) then some very efficient methods exist.