My DD's (now 15mos) stump came off a lot sooner than I expected as well, given my experience w/her older brother. When it did it was much more raw/fresh under than I recalled from DS.
I did mention it to pedi, who said it was fine just keep clean, watch for infection. It behaved exactly as you describe - looking/acting moslty healed, but for many months it seemed there was still a deeper part that was unhealed, and would randomly gunk up for a couple days then resolve. I went to all her well baby visits and would ask about it every time, and was told its nothing to worry about. It did end up finally really closing, though I can't really recall when. Her BB is perfectly fine now.
It always kind of bothered me, but I trusted my pedi, and it did finally just resolve on its own. Hope that helps, but if you're truly worried, maybe worth a check?