My single largest complaint with the entire AWS Serverless ecosystem was that running a multi-region API Gateway was impossible to do. Well, impossible without servers. You could do it if you were willing to run a few nginx reverse proxies and some load balancers for a production quality setup.
This time is over. With the new launch of Regional API Endpoints for API Gateway, the nightmare is over. You can now do Active/Active or Active/Passive failover with ease.
How Easy is Easy?
Create your custom domain in two (or more) regions
You'll need an Amazon Certificate Manager cert in both regions for *.example.com