I agree with Mike, under a larger load the cables are able to deliver the current. Kind of like a clogged water pipe, it can trickle water, but when the faucet is wide open, it can't increase the water flow. Bad/ coroded cables and marginal grounds are can show proper voltage, but inability to deliver required amps.
Not a probable culprit for your issue- a slipping alternate belt will reduce the ability to regenerate amps and deliver ample current. I learned that in 1980 on my 1971 ElCamino, while in high school.