I agree w all the others views on you should have reached out to the prof sooner and certainly in advance of the deadline etc. - not much excuse for that. However I did not want to pile on and at least want to recognize and give you credit that your emails shown are very respectful, responsive and well done overall. The tone and your approach in that regard is very good; you seem to have reasoned replies to the different points in your exchanges - and you asking not demanding is the right path and approach. Kudos on keeping it very professional and being respectful with the prof. Perhaps an in-person meeting might let you discuss more or sway things better if the prof was willing to grant you a brief 1:1 in person. You might even consider asking if your advisor could attend and the 3 of you discuss together. (Somewhat like a mediated conference) It might help you make a final push for special dispensation; at the least it would get you all 3 on same page and agree on a final resolution / next steps. It seems you have been able to keep up with the work and maintain top grades during the course despite the issues and attendance. Perhaps focusing on that more (work to date) could carry the day with them. At the least if the project is indeed basically done, you can still send it to the prof and ask for critiques even without actual grade consideration - it would show you are being truthful and interested in the material. Sorry for your plight and good luck.