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.
I guess where we differ is that I believe that we've tried the other side and found it wanting. You can say that the Biden asylum catch-and-release policies did not include entitlement reform or worker protections so they don't count, but what it shows me is that too many moving parts mean that only the worst aspects of the worst solution are what get implemented. The simplest solution is securing the border and deporting illegal immigrants.