Nginx proxy cache 301 redirects but ignore querystring

We have a lot of ad-based traffic that pass various query string params on the URL, but these do not affect the content/output of the pages.

I currently have the following nginx proxy cache configuration, which passes uncached requests to another backend server that actually returns the content.

proxy_cache_key    "$request_method@$scheme://$host:$server_port$uri";
proxy_cache_valid  200 15m;
proxy_pass         http://backend;

I am just using the $uri and not the $args within the cache key so that both of the following would pull from the same cache, which is working great

http://www.somedomain.com/?aid=129f58ad4af8f9de08bbd6bb7df22850
http://www.somedomain.com/?aid=4db00563d4181dc8d1dfd3b5cd6dc708

But, if I start caching the 301 redirect responses from the backend server

proxy_cache_valid  301 15m;

Then we start caching the 301's returned from the backend server, using the non-arg cache key which causes a problem because:

    the first request to

http://somedomain.com/?aid=129f58ad4af8f9de08bbd6bb7df22850
redirects to...
http://www.somedomain.com/?aid=129f58ad4af8f9de08bbd6bb7df22850

but
http://somedomain.com/ or http://somedomain.com/?foo=bar
pulls from the cache and redirects to...
http://www.somedomain.com/?aid=129f58ad4af8f9de08bbd6bb7df22850

Is there a way to have the 301 redirects cached that ignore the querystring and just passthrough whatever querystring params are present on the request?