I've asked myself the same things and always feel that need to re-evaluate. To me, the date of GP's death would be really significant in helping to determine BL's behavior pattern and predicting his next moves.
If she did indeed die on the 27th, following the Merry Piglets incident, that means BL made decisions afterwards that included leaving the crime scene and van in place, hiking on foot for two days, hitchhiking back to the crime scene, all the while being seen by people and deceiving them by talking about his gf back at the van, etc. That would seemingly be him setting up an alibi before driving away in the same van. Much more purposeful thought put into this scenario, on his part.
IMO, that would be a very different type of person than one who killed GP on the evening of the 29th and immediately fled the scene before anyone could possibly know what happened.
I wonder if his behaviors immediately after her death might give hint to profilers on whether he would now flee and hide, kill himself, or seek help from others.