One way to back up data available today is to start exporting MapReduce, as described here:
https://cloud.google.com/bigtable/docs/exporting-importing#export-bigtable
You are right that today access to the Bigtable Cluster is tied to the availability of the zone in which they operate. If higher availability is a concern, you can look at various replication methods for your records (for example, kafka), but that does add other complexity to the system you are building, for example, managing consistency between clusters. (What happens if there is an error in your software and you skip distributing some entries?)
Using a different system, such as Cloud Datastore, avoids this problem, as it is not one zonal system, but it provides other trade-offs to consider.
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