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I've worked on a similar problem and we have pretty much the same issues as you. An idea that makes things better is having an intermediate representation that exposes the key tables of your dwh and gets compiled to SQL. This allows you to have somewhat better security (even if the model outputs garbage it can't do too much damage because nothing except exactly what you want is even representable), and somewhat better explainability (you can't guarantee the model will get it right, but you can see what SQL gets executed rather than "magic 8-ball says no").

But as you say custom types and encoded domain knowledge is extremely tough and as a result it's very tough to "transfer" the system to different databases.