Amazingly, I also slept through the night last night (and I can honestly say that it was the first time I'd slept through the night since some time during the third trimester when I was pregnant with her... which would put it at sometime around two years ago). I feel so rested this morning!
I want to thank everyone who had advice and ideas on the whole situation! Reading the comments section really did make me feel better.
The way her size 6s currently fit is kind of strange. They're okay when she's standing up. And they're okay when she's sleeping during nap time (which seems to usually be on her side). But at bed time she flips over onto her stomach as soon as I put her down and they just don't work for very long when she's laying that way.
She is kind of tall and skinny for her age (we went to our WIC appointment yesterday and while she only weighed in at 30.6 lbs she was 35 inches tall) so I think the fit at the top of the diaper just may not be tight enough to work when she's lying down. Now that she's weaned and running around like crazy her little milk belly is almost gone (although she eats a ton of food... six times a day!) and I think that's also contributing the diaper fit.
The shape of the 3T-4T Pull Ups fits perfectly though and I was very relieved to learn that some of the brands do actually have pull tabs. Sadie is excited because the new diapers are pink with princesses!
I do think volume was another problem (although she doesn't really drink anything after dinner) but the Pull Ups seem to be handling that too (probably because they are designed for older kids). Sadie does usually drink a couple of sippy cups of milk after she wakes up from her nap between three and four, and while nap time is four whole hours away that's really the only time she drinks a lot all at once (there are always sippies lying around, but after dinner we go straight up for bath time).
So I am relieved by the way the Pull Ups are working out! They are much easier than I imagined when I was busy worrying earlier this week! What a relief!