Can I pre-cook chicken in a sous vide bath while cooking something else?
You can cook chicken at 135F, or indeed any temperature 131F or up. It will take a while; several hours, as noted in the Baldwin Sous Vide Guide you posted. If you pasteurize it at 135F, you can then later cook it, ignoring the temperature (and only worrying about the texture, etc.), as its already cooked to safety.

If you want to hold it, chill it down quickly, e.g., in an ice bath. Do not remove it from the bag until you're ready to throw it in the oven (to minimize oxidation).

I do not suggest turning your water bath up, as you will end up with well-done shortribs instead of the medium-rare ones you wanted.