Alexa Skill - Update Intent programmatically

YES! See Update Interaction Model section at their docs.

https://developer.amazon.com/docs/smapi/interaction-model-operations.html#update-interaction-model

No - Amazon does not provide an API for updating your skill. I believe that API.AI provides this and they have an integration with Alexa ASK but I've heard that it's not very good and I don't really expect it to get better now that Google has bought them.

In your first paragraph it sounds like you are talking about supporting a lot of different utterances (ways of saying the same thing), but after that it sounds like you are talking about a large number of 'slot values': the relevant user input extracted from the utterances. Either way, the answer is still no - no API.

I believe there are popular features requests for both a general API for updating the skills, and support for dynamic slot lists, here.

And here's Amazon's defence of the custom slot and how it can replace the (deprecated) literal slot.