Aren't you basically describing SSPL? That's MongoDB's license that does pretty much what you're describing, except it's not considered open source [1]. And in response, Amazon created an API-compatible alternative called DocumentDB [2]. There's also the Commons Clause [3], which I think Redis Labs uses to license its Redis satellite products.
This looks like a great case-study. Basically, it seems that if the licensing isn't in Amazon's favor (take the OSS project, put it into operation, sell it as a service), then Amazon is likely to simply build their own implementation that is API-compatible. It remains unclear whether the ROI for this exists, especially for larger/more complex projects, but the precedent is very discouraging for my idea.
[1] https://www.zdnet.com/article/mongodb-open-source-server-sid...
[2] https://aws.amazon.com/documentdb/
[3] https://commonsclause.com/