I found Amplify excellent to get up and running quickly. I’d highly recommend it for anyone without a well-oiled CICD setup who wants to quickly get a website up to test out an idea.

Unfortunately, I quickly hit the limits of its configurability (particularly with Cloudfront) and had to move off it within a few months.

You could just use Amplify for the backend and pair it with any other front end host / CDN provider. I've used it with Vercel and it works great.

Care to elaborate on the limits you hit?