Ubercart- Assign new role on expiry
It seems that "I am unsure on what action to call this rule" is your remaining issue, and that by using the rules module you are already close.

However, when talking about Rules and its Event-Condition-Action concept, your issue is about what Event to use. With that in mind, I would try to use the Rules Scheduler submodule of Rules, to schedule the rule to be executed at the moment of the purchase already.

Makes sense?