Well, good news. I talked with my dad, who works with engineering specifications of this sort for a living. If I understood him correctly, which I think I did, and if I've read a few wikipedia definitions correctly, which I think I have, I've determined that a 2x8 will be adequate for my ceiling joist span.
Mostly as a future reference to myself, but as general information for anyone considering their own span, here's a few good links.
First, the weight of drywall - according to the first good search result I found - is 2 pounds per square foot. http://wiki.answers.com/Q/How_much_d...alf_inch_weigh
Even doubled, to 4 psf, that's a rather low dead load (remembering that my ceiling joists are like attic joists, with no floor laid on top).
Take that information and go to American Wood Council's online span calculator. Link
Choose the species and grade I was instructed to (southern pine, No. 2), choose the member type (ceiling joist) and the spacing and sizing requirements of your application (in my case, 24 inch spacing, 2x8, and the smallest dead load option available) and the deflection limit you can tolerate, and the calculator gives you the maximum span. For my case, even assuming 10 psf dead load which is likely more than double my actual dead load, a span of more than 12 feet is manageable with a deflection limit of L/480.
What does that mean? Well, it means that even if I used four layers of 5/8 drywall, a 12 foot span supported by 2x8 southern pine wouldn't sag more than .3 inches. I can tolerate that!
I know I skipped the deflection limit calculation. Here is it. Deflection limit is given as a fraction (L/480, in my case). The span (L), 12 feet in my case, (I'm rounding a little) divided by 480 gives the total deflection. 12/480=0.025ft. 0.025ft x 12ft/in=0.3 inches or just under 5/16 inch. Ta Da!
I'll see if I can find someone to check my work here.
(Edit: my number for the weight of drywall was wrong for 5/8 gypsum. It's actually just over 2 psf - appox 2.2. That won't matter in the slightest, but it does make me more confident that I don't want to try 2x6.)