I've driven by myself a few times over long distances like that where the objective was 'just to get to my destination' and what I'd do is pretty much be on the road 24 hrs but I'd stop at Wal-Mart or rest areas every few hours for food and rest and during the night catch 2 or 3 hours of sleep before getting on the road.
Everyone is different but this works well for me and I can probably drive a good 16 hours / day like that.  If I try to drive non-stop and then stop for the night, I don't think I can do much more than 10-12hrs / day.
As far as 95 vs 77, my vote is for 77.  We decided to do 95 at XMas because we were worried about snow in the mountains along the 77 and really regretted it when stuck in heavy traffic on the 95.