Agreed.

Everything else has been ruled out. The lift pump must be marginal........works fine for all conditions except maximum power.

My only reservation is the term "lengthy" for the hills. If the pump was the culprit, the problem would show itself very soon after maximum power is demanded on the hill. If there is a delay in the onset of the symptom, then I might think again with regard to the pump.

In any case, the pump has a specification for flow rate..........worth checking.