If I were you I wouldn't apply with them again for some time. You've already been denied multiple times and not enough has changed with your profile to increase the odds of a different decision being yielded if I'm being honest.
I have a 90 day late and a 120 day late one 2 different accounts and I was approved for Discover about 3 weeks ago, but I also have an AAoA of 7-8 years with my oldest account being 16 years... and I only had 1 inquiry and no accounts opened in the last 15 months. So, they definitely were able to overlook my baddies as everything else was pretty solid.
I think your best bet is to age you file for at least another 6 months but preferably a year without applying for anything (or much) else. With your AAoA growing a year and no new inquiries along with past inquiries falling off I would imagine your chances will be much greater. Your score will probably be 40-50 points higher too which of course is indicative of better chances of approval.
