The heroku-> lambda path is what I was considering - so would love to hear more about any pain points etc. edited nvm read claudia.js. Reviewing that vs apex.run now. Thanks for open sourcing that deployment tool.
another thing is that although Api GW can behave like a web server for most things, some things are more restricted than with a fully programmable server. for example, you need to declare all HTTP response codes upfront, so that the pipeline can be configured. There can be only one success code (so eg returning 204 when there is no content and 200 with content from the same endpoint isn't trivial).
the third thing, that several commenters mentioned on this page, is that if you want to use API Gateway, processing binary data requires S3 or something else for storage. We currently let people convert files by using ApiGW + Lambda to get a signed URL for S3, then post to S3, another Lambda converts it into PDF and saves back to S3, and the client polls S3 to pick up the result. It's fantastically scalable with that design, much better than posting a file to heroku and then getting a synchronous response, but it takes a bit of rearranging the code to work.