Sorry... I have more energy during the day with less carbs, but I still definitely need 8-9 hours at night. I don't feel well on less than 6.
I understand the feeling though. Are you breastfeeding? The one thing that was a lifesaver for me when my son was a newborn was to learn to nurse laying down or in a recliner with him on a nursing pillow, so I could sleep a bit while feeding him. It's rough when you have a poor sleeper... my son spent his first 6 months or so sleeping in my arms, so I totally understand! If I hadn't been able to doze while holding him, I might not have survived it!
Hope you find something that helps!