Kiskaloo:
The failure rate of batteries once returned to service will need to return to the one-in-a-billion chance per flight hour as I believe that is the certification requirement.
Perhaps not if the fireproof box reduces the criticality of the failure. If it can be demonstrated that it is safe to continue flight with a smoldering battery, then the 10E-9 per hour requirement can be reduced. Of course, this depends on whether Boeing will demonstrate containment for some period of time vs permanent containment.
As for ETOPS, that's cutting it pretty close with probabilities. Now its not a probability per hour figure, its a probability that the battery will/will not be available during some flight beyond a range from an alternate. Which is probability per hour times that range (in time). The difference between no ETOPS (a 30 minute diversion range?) to ETOPS-330 is 11:1. Cutting probabilities that close is a dangerous game. In other words, if you can't tolerate the APU battery loss with a 330 minute diversion, you can't for a 30 or 60 minute diversion either. Which pretty much means no flying. On the other hand, if the RAT provides a non-time limited critical power source, then the APU is not a factor anyway.
Same thing goes for the main battery. Look at its braking function. That is a non-time dependant requirement. No matter how long the flight, you need the same braking power at the end. If the probability of failure during a 330 minute diversion is intolerable, then a factor of ten isn't going to buy you more safety.