S3 offers custom error pages through the web site endpoints -- but not the REST endpoints... but signed URLs only work on the REST endpoints, and not the web site endpoints.
So, no, there is not a way to directly solve this using only S3.
One option is to use CloudFront, which offers the ability to replace the standard error pages with a custom static page, but the error content is lost and all you have is a static page. You also have to use the CloudFront URL signing mechanism, which is different than S3 (though it also has some advantages, such as wildcard support in a signed URL).
In this answer to a question that is similar, but not a complete duplicate I demonstrated the way I've used an XSL transform to "style" the S3 error XML, by modifying the XML returned to the browser, injecting a link to the XSL stylesheet, and letting the browser do the rest of the work... see the screen shots.
I'm quite pleased with the solution, though it has what some people would consider a drawback -- it requires all of the S3 requests be served via a proxy server running HAProxy in EC2. There's a small additional cost for the EC2 instance, but no added cost for the bandwidth, since the transfer from S3 into EC2 is free, and the transfer from EC2 to the Internet is the same price as transfer from S3 to the Internet. With this setup, the S3 signed URLs still work. The additional advantages in my application us that this allows me to use my SSL certs with S3 static content (although this capability is also available through CloudFront), and the fact that the proxy's access logs are in real-time.
