Sorry if this sounds dickish, but renting 3 servers @ $75 apiece from 3 different dedicated server companies in the USA, putting TinyDNS on them, and using them as backup servers, would have solved your problems hours ago.
Even a single quad-core server with 4GB RAM running TinyDNS could serve 10K queries per second, based on extrapolation and assumed improvements since this 2001 test, which showed nearly 4K/second performance on 700Mhz PIII CPUs: https://lists.isc.org/pipermail/bind-users/2001-June/029457....
EDIT to add: and lengthening TTLs temporarily would mean that those 10K queries would quickly lessen the outage, since each query might last for 12 hours; and large ISPs like Comcast would cache the queries for all their customers, so a single successful query delivered to Comcast would have (some amount) of multiplier effect.
Even a single quad-core server with 4GB RAM running TinyDNS could serve 10K queries per second, based on extrapolation and assumed improvements since this 2001 test, which showed nearly 4K/second performance on 700Mhz PIII CPUs: https://lists.isc.org/pipermail/bind-users/2001-June/029457....
EDIT to add: and lengthening TTLs temporarily would mean that those 10K queries would quickly lessen the outage, since each query might last for 12 hours; and large ISPs like Comcast would cache the queries for all their customers, so a single successful query delivered to Comcast would have (some amount) of multiplier effect.