Please help!!! Missed admissions deadline by a few minutes for target school, how to negotiate!!!!

Nice_home

I'm purposely not including a lot of details since I am actively trying to revive this application with the target school!

Long story short, after a brief email discussion with target school's admissions office to go ahead and apply through LSAC even though late, I still missed the (late) deadline by a few minutes. (Full disclosure: I acknowledge that the lateness was totally my fault.)
The next day, the same admissions office who just a day before said go ahead and submit it quickly, came back with, "Unfortunately...." when I asked if I could submit a copy of the app via email instead. (I have a complete copy of the fully downloaded application from LSAC.)

Another higher ranked school has already processed my late app, and another one, though I didn't receive an acknowledgment email from them, already requested the CAS report from LSAC, so I believe they are in the process of review. However, those are not the target schools.

Does anyone have any experience with this? Or even if you don't have experience, can you please help me with ideas about how to negotiate the target school back into accepting my late app?

Thank you in advance!!!!!!!!!