Gonna really, really,really reach on these, but, what the hell..
If it was electrical, as in the angle of the hill made some wire / connector, lose contact, then why didn't it immediately go back to running the way it always did once back on flat ground? Hmmm... It coughed and sputtered, almost as if it had sucked something nasty ( like water ) from the tank, and had to clear it out of the fuel lines. As water lands up at the bottom of the tank, if there's any in there, it may only be hitting the fuel pick up when the car is angled up on a steep hill. Fuel line anti-freeze works by absorbing the water in a fuel system.... Yeah.. that one is definitely a " stretch"
Climb the hill, let her die (as you pull over to the curb). Disconnect the injector fuel supply and then pump a bit out into a suitable container for inspection. That would establish fuel supply and quality.
Will it climb the hill in 2nd gear ( put the shifter in 3rd and press the "manual" button in). If it will, it would seem to indicate that an electrical communication issue between the TCU and the ECU.. Damaged speed sensor lead? You did mention a "thunk" and her dying out, pulling into the parking lot. Intermittent short?
Will it climb the hill in reverse? That goes back to condensation in the fuel tank.
Disconnect the battery..
it's not "voodoo magic".. Think of it more as an exorcism
