Shortly after I last wrote about this, we really turned a corner. Right around their 13 month birthday - just as they were both in the 18 pound range - they suddenly started both sleeping through the night with some consistency. The moral of the story: it'll happen eventually, and just as you can't force your underweight kid to eat, you can't make them sleep.
Now, I'm still tired. We have good weeks and bad weeks. Thing is, while they sleep pretty well as a whole now, and have for months, they don't sleep well when sick (hi, ear infections) or getting a tooth (in the last 8 weeks or so we've sprung 7 molars, three of which are just barely broken through the gum. If you're counting, that means we have 9 teeth left before the two year old molars -which I'm just going to assume will come in around 3, and I like to think of there being 9 left and not 15 - and 3 more to finish breaking through the gums). On average, I'd say we have nice solid nights sleep around 4-5 nights a week*.
*I should go to bed earlier though, since they still get up at 6:30 on average :) I imagine this would help with the vague sense of ongoing exhaustion.