Apparently, if I don't try to create a production-ready project from the start (by that I mean a lot of fiddling with AWS services) and take a step-by-step approach, everything becomes super easy.
Most of the frontend is ready, just a few forms left to do. Backend is pretty much ready, I might need to update my models, but it's easy. I have a few issues with uwsgi and docker, but it's not a dealbreaker, so I can skip solving that for now.
GraphQL works great and I love it! The last step for MVP will be to write a full Schema and connect Frontend with Backend.
Maybe I will fiddle with CloudFront, S3 and other AWS services for a proper deploy, but it's not an essential step.