Is there any way to setup a URL to act as a router to these different
images? The routing URL should be indexed by search engines.
The most efficient and affordable way to accomplish this is to use a content delivery network (CDN), which would cache your images on servers around the world, and serve them from the server located closest to the requesting client, without any additional bandwidth costs.
As indicated from one such CDN, CloudFlare:
CloudFlare operates out of 23 data centers around the world. Our CDN
automatically caches your static files at our edge nodes so these
files are stored closer to your visitors while delivering your dynamic
content directly from your web server. CloudFlare then uses a
technology called Anycast to route your visitors to the nearest data
center. The result is that your website, on average, loads twice as
fast for your visitors regardless of where they are located.
On average, a website on CloudFlare loads twice as fast for its
visitors, sees 65% fewer requests and saves 60% of bandwidth. You’ll
be able to see the exact speed benefits and savings with your
personalized CloudFlare analytics report for your site.
We never charge for bandwidth
Using a CDN, your image URLs would remain the same, without the need to route them to backup servers.
The other ideas presented would likely not play well with search engines; they might view them as an attempt at cloaking or other black hat technique, potentially resulting in penalties.