Could you elaborate on this? Assuming the chosen period length of 5 s for the beacon chain, what average time to failure does that correspond to? How did you work out this assumption?

I think you mean by 2^9-of-2^10 committees that 2^9 out of 2^10 notaries per committee must sign off on a proposal for it to get through, not 2^9 referring to the number of shards. Source here. AIUI, if we assumed a 50% honesty assumption, that would mean that if half of notaries went offline, all of the remaining half would have to sign off on a proposal to get through, which seems unlikely, so we either have to assume that this is unlikely to happen, or the proposal may be delayed until more honest validators come online (assuming that some of the remaining half are malicious).