You should have made your intentions of requesting a letter known near the end of the semester when you still had regular contact with the two MIA letter writers. Professors are ridiculously busy and hard to get ahold of, and they may even be on summer vacations.
I asked all of my letter writers for letters in January/February and told them my intention of applying in June in the coming summer, a few weeks to a month is not enough time to ask for a letter in my opinion.
You have really no options and this is a difficult situation. You need to send another email to letter writers 1 and 2 directly requesting a meet up to discuss a letter of recommendation, it's far too late in the game to be political about the situation and vaguely ask to meet. I would also make sure that letter of rec is in the subject of the email. Good luck, I hope it works out for you