You can publish the rewrite.config to the broker and extend something like the URLRewrite.NET module to load the configuration from the database instead of the filesystem. The cool thing is that you can use it ahead of the DXA Static context module and before DXA starts processing the URLs.
One thing to consider is how you are loading the config from the broker since you could have many topology websites with multiple web applications hosted as a single website in IIS. Coming up with regex patterns for all of them and managing the configuration would be key to keeping the solution scalable.
A poor man's solution would to have a Razor template (or anything for that matter) publish a custom extension to the deployer. You can then configure your deployer to copy the custom extension to a filesystem instead of the broker database. You can include this in your IIS module for it to be picked up OOTB, This would still work but need to consider scaling among other considerations / configuration. Hope it helps!