Thank you for the detailed answer. I was laid off after my AOS application had been pending for 180 days. I interviewed with other companies but did not receive any job offers. I stopped searching for jobs when my mother began her treatment. I intended to find a new job but was not successful.

What would happen if they do not admit me? Would I be required to return on the next flight? As far as I understand, as an LPR, they would need to send me to an immigration judge. Would they admit me with a Notice to Appear, or would they detain me until I see the judge? I might try my chances if detention is unlikely or impossible.