My thoughts on this have always been a blend of your two 'they should not be deported' scenarios, with a slow, measured rollout.

Sudden changes cause too much chaos, and you don't always know what works until you try it. Avoiding entitlement abuse is always going to be part of the conversation, and it seems to me the fix for this (and nearly any other issue) needs to be approached carefully from both the supply and demand sides until what's effective is more clear.