I just don't understand why it's necessary for the ex to back off in order for your relationship with your DH to blossom.

I would expect to hear a jealous rant from dh about this too. It's not as if his accusations are completely baseless. No, I wouldn't think you should take the accusations lying down but it seems you are more interested in defending your friendship with someone that 1) you used to know intimately and 2) appears to be the one you go to when things go wrong with your marriage.

You are not addressing his insecurities at all. Imagine how crap dh must be feeling if he truly thinks his wife holds a candle for another.

Turn the tables a bit. Put yourself in your husbands position. If you knew he was secretly meeting his ex for lunch (specifically to talk about your personal issues), that he kisses this woman and that she told him it was clearly because his needs were not being met. How would you take that?
I would sit him down and discuss what the problem between him and me !