We ran into the same issue and we had to use API gateway to rewrite urls. but it had the added benefit of handling CORS there and the preflight requests never hits the application servers. Additionally preflight requests are cached at cloudfront and at browser with "Access-Control-Max-Age" and for the first request we do pre connect during the main domain load so the users never notice the small latency it may have.

I agree that AWS products are all over the place.