I agree wholeheartedly. "Best practices" suggested by AWS, GCP are to architect these services with one function per endpoint, with API gateway handling the routing. Sounds good but if you need reasonable tail-end response latencies in the event of a cold start, you need to forget all about the serverless abstraction and go back to a single container with all of your functionality.
On the other hand I can see the appeal of one instance, one request. I don't know if the answer is to enable (optional) request parallelism or to optimize cold start times down further, but OP's requirements feel like they are way too modest to basically force them out of the serverless paradigm.