Could you pump after feeds during the day, so someone could do a syringe
or
cup feeding at night, letting you get in 3-4 hours of sleep at a stretch?
Since Alli can't nurse yet, we're doing all feedings with EBM now, but I
do
know that when we stopped trying to have her nurse and went to pumping and
feeding EBM (which let other people feed her), which let me get a longer
nap
at least once a day, it really helped many of the PPD symptoms I was
starting to show. I can't go longer than 4 hours w/o pumping, but the
difference between 2 hours or less of sleep and 4 hours is dramatic.

there are certainly tricks you can do to juggle things, I find that I would
wake at night anyway, having someone take ds out in the afternoon whilst I
napped was great, but I only managed to make that happen once or twice, but
it did have a noticeable affect in delaying things.