FWIW here is my riff on things.
HG gets seriously lost when leaving that second party as she attempts to walk home. This seems crazy, but based on what I have lived through and seen in others when extremely drunk, the more familiar you are with your surroundings the more confused and disoriented you can become. I call it the Privet Drive effect (see Harry Potter). You are more complacent when comfortable with where you are and houses, apartments, cars, porches, street corners, and doors all sort of look alike worsening your disorientation. At 11:50 or 12:15 she declares she will walk home alone. Although a mere block from home, she makes a wrong turn and doesn't see her building, but she doesn't notice. She only feels it is close; no worries, so she keeps going. Even though she gets further from home, all is good because it is all residential it lulls her. Kinda like getting lost in a desert; being surrounded by what is familiar and the same, but instead of endless sand, it is rows of houses with some apts. It is hard to notice how much time has elapsed, and you are so focused on getting home like you do all the time; nothing feels "off'. Each corner will be "her" corner until she is utterly lost. She really has no idea of how far she is from home or how long she has been wandering.
I think she is by now texting friends, and when she gets to McGrady's it is SNAFU because she has walked out of her comfort zone of residences. She actually looks most vulnerable and scared at this point, IMO. She has no clue where she is and hence the seeking behaviors. She is relying on her phone to help, and trying to be casual about looking to street signs. She is so intent on orienting herself she stumbles off the curb. She goes toward the entrance maybe to see if a menu is posted or something to help her figure out how far she has overshot home and where the heck she is.
An employee offers help, and HG gives him an "I am just walking", but she doesn't say share her full intent which ends that sentence with the word "home". In her mind she is just walking home; no biggie. I thought it weird she would decline help, but I think that based on how she was portrayed in media, this is not at all unusual. HG is extremely self reliant, exacting, and in control; besides we are all invincible at age eighteen. She also knows that adults or authority figures expect her to not end up in this situation, so she kinda tries to downplay she is lost to others. She is only comfortable being that vulnerable with her friends.
I sense she runs at the Shell station not because it is dodgy, but because running helps her sober up. If she is going to get herself home, she needs to suck it up and get lucid. An athlete knows that running will release endorphins and clear up brain fog super fast, and she has done this before.
It worked! By the time we see her on the DM, she has a long, confident, purposeful stride. I now see purposeful more as her conviction to get herself home. I also sense she is "faking" it a bit. Inside she feels scared and out of her safety zone, but she needs to keep it under control because that is how she rolls. I just had the thought too that maybe a friend suggested she go the mall because it is lighted, more people around, and to walk around to get her bearings and they would text her back home block by block. It also helped to be in bright, less familiar environment; she is out of that lull zone. It helps continue what the running started; the adrenalin keeps flowing which further clears her head.
As for talking to JM, he was not an authority type but seemed like he could have been a student. Maybe she told him she was lost; what else could she do now that her cell battery was done for? He could have said, as luck would have it, he used to drive a cab, so he could get her home or drop her near there. I think he likely bought waters for them, btw. No way HG would have added more alcohol to the mix at this point.
This is full of holes of course, but this all that makes sense to me.