Sucks that you are in this situation
Curious to know, which immigration lawyer did you use? Most of attorneys that came up in the chat room (e.g. Goldstein) comes at $5000 minimum. At least that was the quote I received back in July 2023.
Like many members here, I have attempted to build a case through ways you described above. At the end of the day, there was minimal impact to timeline. I emailed the consulate requesting reason for denial - ignored. I emailed to explain in detail hardship (e.g. family separation, financial burden, loss of job opportunity) - template response. Also emailed congress/senate representatives... even the White House - got bounced back to DOS and received a SOL response.
I know I sound super jaded having been in AP for 10 months.