Engine dies when I step on the gas

When I push hard on the accelerator to go up the hill, the engine cuts out the instant when the car should downshift into first.

Are you at the bottom of the hill ?
Or part way up all ready.
You said long hill. You did not say steep hill?

Ima thinking accelerator pump circuit; but
just for kicks, leave it in first to climb that hill, and keep the throttle open enough to climb at a steady pace, neither gaining nor losing speed.
Then report back.