There's two places you'll need to change this. The first is in the package.json, which now contains a load of useful custom commands for building and generating your app. You should see a line like this, defining the build:browser:serverless commmand:
"build:browser:serverless": "ng build --prod --base-href /production/",
Remove the --base-href /production/ part. If we were sticking with our long, cumbersome API URL we'd probably want to keep it. But we're not.
The second is in the serverless environment file (src/app/environments/environment.serverless.ts). You'll see that there's a base href in there set to production. You just want it set to /.