You quite literally have to play MC oblivious and dismissive of Liz to get anywhere near the Happy or NTR paths. To me, the lovers path is the most in character path, since, as you said, MC acts foolish on the others
I see your point, however, let's look at this from Liz's perspective on the NTR route:
She just found out that her new manager violated her and is now blackmailing her with her relationship and her job on the line. She can't tell MC the details, because they haven't been together that long, haven't even had sex. Liz is also a virgin in her early 20's, a wallflower who has little to no experience with men.
Now, when she really needs her BF to support her, he dismisses her and pushes her straight back to her abuser. He doesn't pick up on what's bothering her whatsoever.
Liz therefore learns MC is neither dependable, nor does he care enough about her to inquire about her problems.
Matt is also a very charismatic person and great lover. Why should she resist him for the sake of MC who doesn't really deserve nor care about her, from her perspective?
On the happy route I'm more with you. However, I do think she shows her disdain. She's extremely troubled when MC finds her after the club BJ with Matt.
She also really tries her best to please MC the weekend after the camping trip.
So, while I think Liz' characterization could be improved, it's nowhere near as bad as you make it out.