I have the same problem as the original poster. If I am up and moving for an hour or two before the shave, I get a nice 24 hour shave. If I shave upon awakening I have stubble an hour later, stretched skin or not. Most safety razor bars/combs do stretch the skin just ahead of the cutting edge.
So my opinion is that my facial skin is swollen / fluid bearing until circulation redistributes the fluid. The cold water shave mentioned above is a good idea...but...I started Str8 shaving to enjoy the process!
Anyhow a good scientific wild a** guess! YMMV
~Richard