The world has enough fixed gear bikes, but nowhere near enough PX-10s in good, ridable condition.

If this were my bike I'd swap out the derailleurs for Simplex Super LJ types, then locate some new sew-ups (preferably fat ones by Challenge, Dugast or Conti) and mount those. Chainrings are still available for the Stronglight, so you can replace those easily enough. Other upgrades you could do here would be to mount the Simplex ratcheting shifters, or (better yet) try to locate some Suntour barcons or Campagnolo bar-end shifters.

Lastly, a Brooks Professional in place of the original ass-hatchet Unicantor would be a nice touch.