Hi Bob - yes King's Catechol formulas are reportedly fine for rotary/continous agitation. I can vouch first hand for PMK working because I've tried it (it's in The Book of Pyro too). I believe the split development technique you mention is also recommended in his book. It is a good way to use dilute developers (such as PMK) in a Jobo since depending on your machine and tank you may or may not be able to use enough solution volume. I'm not a Jobo user myself but my understanding is the Jobo systems were really designed for minimal solution volumes.
Nicholas is correct. Further to my previous post, most "modern" staining formulations (like PMK, Wimberley and Pyrocat) contain an additional developing agent and are less sensitive to aerial oxidation problems. However the more traditional formulas containing only Pyro (or Catechol) as a developing agent, that are designed to induce imagewise stain (ie contain minimal preservative) won't work in a Jobo. ABC would be an example. It barely works in trays. Note you can make these developers more stable by increasing the amount of preservative - but then you get less imagewise stain. One of the key attributes of Pyro developers such as PMK is that through careful balancing, imagewise stain is maximized while at the same time it is relatively stable. Rollo Pyro is apparently more of a compromise developer. It was designed to work with rotary processing but produces significantly less imagewise stain than PMK or Wimberly.