This question largely stems from the fact that I'm not 100% sure how Overrun works in general. Let's say I have a character with Barreling Overrun. I understand that I can Overrun through anyone as long as I continue along a straight path. But, can I combine this with a charge and make an attack against someone at the end of my movement?
Yes. As stated in the entry on the Overrun action:
As a standard action, taken during your move or as part of a charge, you can attempt to overrun your target, moving through its square.
So you can use Barreling Overrun as part of a charge and get your attack at the end (the Overrun action does not specifically remove it).
The RAW in this case is badly mangled however, so in reality almost any interpretation could be valid, and as far as I'm aware Paizo has never released an errata on this point.