Practical aspects -- how to change subfields between PhD and postdoc?
When would be the best time to do this catching up? If I do it after beginning a postdoc, my postdoc work will be delayed during this (probably months) of catch-up time.


A piece of post-doc advice that has worked for me is to have your fingers in several pies. Build up some new expertise while working on some low-hanging fruits from your existing background that will lead to immediate results.


  If I were a PI, I would favour candidates who had demonstrated a capability in the field already. How can I demonstrate an ability to do theoretical work if it was not a large component of my PhD?


The qualities that advisors are looking for may vary significantly. If they are looking specifically for a candidate with a strong theoretical background, there's only so much you can do. Others will prioritize broader research skills, like


a strong ability to finish projects (which you can show by building an appropriate track record; so be sure to have your pending papers out before you apply), and 
a strong ability to tell a good story (which you can show by being outstanding in your application materials and communication to them; basically, explain how you will help their team succeed based on your expertise).