Carita--kerc is right. Just start doing your dissertation if you want it done. I'd probably say no to the conference unless it literally involves a chapter of your diss (preferably one you haven't written yet), especially considering that you sound pretty strapped for time.
I need to take kerc's advice too. I had a good week where I dedicated myself to writing 5 sentences on my article each day, and then we got hit by the snow days and the sick days (first R, then me) and more cold and it all gave me great excuses but it didn't get the article finished. I'm going to start this week with a renewed commitment.
On the student who turned in late work: I do state it, somewhere, I think. It's the online class so I don't personally write the syllabus, as we have several sections, but I think I edited mine to say something along those lines. What should help is that there's a week-long grace period on each assignment and after that it closes so students can't submit it anymore--which should signal that I'm no longer accepting assignments at that point. My classroom syllabus does state it, but won't do me any good in this situation.
At any rate, he emailed and I explained that we don't accept work that's three weeks late, and I ended up telling that to another student who tried to submit too. Haven't heard anything yet so hopefully it's done.