I think you need to take some proper advice on this as soon as possible.
It's my understanding that you can't just decide to repeat an academic year, otherwise any student who did badly in a particular academic year could simply re-do it to get better marks. We know that just doesn't happen.
If the Board of Examiners offers you the chance repeat the year, there will be stipulations. For example, marks already attained at a pass level may carry over, and other assessments, including non-submission and fails, may be capped. Obviously, if you have extentuating circumstances accepted, any outstanding work will be open marked.
You will also, presumably, be offered a chance to submit work over the summer. If you don't do this, you will probably need to resubmit your extenuating circumstances application to ensure that modules taken in the repeat setting aren't capped.
I can't advise on whether or not to submit the project you have mentioned. It's too complicated a situation to give reliable advice.