Hi,
Unfortunately I have bad news for you, I also have a "Battlefield V Definitive Edition" as well as the same issues regarding the class assignments. I have personally contacted EA support several times over the course of a year, using different contact methods and with different people. In all of my chat sessions or email correspondence, I have been promised my multiple missing items to no avail. It should be added that I have also been exceptionally patient and as polite as humanly possible, never once coming close to being aggressive, although I had every right to be treated that way. To sum up, it's unfortunately impossible to get the missing items because the team that knew how to manually add them to your account is no longer there. No workaround will work in this case, I wish you luck with EA support, it's always something, but the chances of getting your stuff back are close to zero I'm afraid. I am open to hearing from you if by some miracle you do get your stuff back. I hope that even though my message was a bit depressing, I have shared my unpleasant experience with you so that you don't waste your precious time. I hope I am wrong and you do get your missing quests.
All the best.