About the Bais Halevi’s vort.
You forgot to adress the second issue of the shevatim’s behavior.
The Bais Halevi says that Yoseph gave them mussar. Is my father still alive? You worry that he will die because of Binyamin, but is he still alive because of me!
We still need to understand the shevatim’s behavior. The truth is that Yehuda did a major teshuva. Through Binyamin he repaired the split between the sons of Leah and Rachel. This is why Yehuda became an areiv for Binyamin, and he was moser nefesh for him. This is why Yaakov later said to Yehuda, “from the ripping apart of my son you have arisen.” Although Yehuda was not that good in regard to Yoseph, he arose from that by fixing that sin through Binyamin.
This is also why Yoseph did his whole trick. He wanted to see if they would be moser nefesh for Binyamin and fix up the sin they did with him. Once they did so, he revealed himself to them.
Yoseph nonetheless gave them musar for not being good with him, because the pain they had from his mussar, feeling now more than ever before the pain they caused their father through him, further repaired the damage they caused.