Hi Tom,
The only thing that could help in this case is to keep your solution "suspended" while your are not using it. This could help you reduce your AWS costs to a large extent.
People often forget to implement this simple cost-saving measure and since their solutions are running all the time in AWS, their billing counter keeps ticking. You could either use scheduling options within CAL or do this yourself manually.
Lemme know if this helps.
Best Regards,
Adarsh