I can further narrow this down: I have isolated the problem to a 25-page section that is nearly all tables, some of which span 6 pages.
Having deleted that section with CS5, I can now modify the table style in CS6. I couldn't delete those pages using CS6, as even trying to delete the pages caused the spinning circle.
It's likely a problem with the text itself, or a style. I'd try exporting that story to InDesign Tagged Text and re-import it to see if it works better. Wouldn't hurt to rplace thtext frames, too.
Thanks for your reply Peter. I hadn't thought about the tagged text route, probably because I've never had a use for tagged text!
I gave it a go, exporting the whole of the troublesome section as tagged text. Placing it back in to a new InDesign document with automatic text flow on, I got the same crash/spinny-wheel-causing-me-to-end-task. I tried it again, but this time turned off autoflow and did it page by page, noting the point that it would crash. Next time, I cut out the table that the crash would occur on when I got to it (the crash would happen as soon as I clicked the out port), pasted it on the side, made a note of where it went and continued to place the rest of the story without a hitch. I could change the table style in this document no problem.
I pasted the troublesome table back in, tried to change the table style and got the crash. Right, getting somewhere.
I opened up the previous template, and put back in the section that wasn't causing the problems (everything without the dodgy table). I could change the style fine. I then made a new document, and pasted only the bad table, figuring that it would crash when I went to change the style. However, I could change the table style just fine!
So, figuring that it was all ok now, I copied the table, pasted it in with everything else, went to modify the style and... spinny ball.
Finally, I converted the table to text, pasted it into the main document, and converted it back to a table. So far, so good. I'll update again if I run into any more problems.
Realistically I could have set the thing again in the time it's taken me to troubleshoot this, but I'm a little scared that this happened at all with a document that works just fine in CS5!
We get more reports than I'd like to see about converted files. The only advice I have is to never convert a .indd file directly. Export the original to .idml. then convert that. It's not guaranteed, but far safer than the alternative.
It's certainly a problematic observation, as should we ever decide to leave the safety of our "guaranteed" CS6 for the CC, we'll be moved to a new version whether we like it or not and constantly having to convert files. I don't like that story!
For the next tender we do I'll be sure to create a template from scratch, rather than use the old tried 'n' true as I've been doing.