I've got an invoice layout where I sub-divide our billable items by category, and I'm trying to see if there's a simple way to prevent the category heading (leading sub-summary part) from being orphaned at the bottom of a page while the items it pertains to break to the following page?

I've been staring at this for way too long, so hoping someone can either point me in the right direction or tell me it's hopeless so I can move on. :P

Unfortunately no, at least not reliably. You can instruct FMP to break the page after "n" occurrences of the subsummary, but this is only useful if the parts are roughly the same size.