Interesting. Sounds like Parse wasn't nearly as mature as they made themselves out to be. I'd have expected at least PaaS levels of stability—by, at the very least, pinning each client to a particular API version with guaranteed semantics until they choose to shift to making requests on higher-versioned equivalents of each API resource.
A thought: if "Parse" had originally just been this open source Parse Server offering, and you had taken that and plopped it on e.g. Heroku, would that have been a better deal for you? Seems like "apply FOSS to PaaS to get BaaS" wouldn't have been that much more hassle, operations-wise; and you would have been able to upgrade the backend only when you liked, rather than having it mutated out from under you.