Hey guys,
Thanks so much for these very helpful posts. I had indeed wondered both about using InstanceClassifier and just putting the class on the diagram, and what the pros and cons of each were.
I think I may well go with linking the class directly to the diagram, rather than using the Data Object (taking the point in BPMN it is only available for the life of the process). My model is strictly a descriptive one, intended to communicate to business how the process and data work together, but also for developers to see what data should be used, and therefore what data access/updates are required. I agree Ian - it's not a religion.

The only downside is that I may need to refer to more than one class for an activity. For example, if I have a typical Order and Order Detail structure in my class diagram and the process is to "Create Order", then I would have to associate both classes to the process, which might be messy in complex processes. Or, I could just link the "parent" class of "Order" to the process and thereby imply that "Order Detail" is involved. Or, I could create some kind of container class that links to both "Order" and "Order Detail", which is what I was thinking the Data Object could be.

I suppose the other choice is what Helmutt suggested - use Data Object and then create <<trace>> relationships between it and the one or more classes it represents.
Thoughts?
(Thanks so much for taking the time to think about this.)
Tim