Thanks Murtuza. I think the root cause was both the existence of the limit and the fact that it isn’t very visible within RDS. Without having read thoroughly through the RDS Limitations Page, there would be no way to know that this limit existed or that we were approaching this limit. As a customer of a hosted database solution, I would expect that information be made available to me in the form of an alert, a log, monitoring, or some other means. Having said that, I want to be clear that the responsibility falls on my shoulders.
In our post-mortem review we agreed that this is an extremely rare scenario that will not recur, and rather than focus on prevention we would make sure we had a strong DR plan moving forward.