Power steering overrun - lack of flow or worn box?

I've had an electric power steering pump on the car for about 3 years, info about it here.

It has been just fine for around town driving and parking lot work. If you are turning the wheel fast, it seems to be easy to overrun the pump and lose assist. I took the car to an autocross last weekend and the power steering was effectively useless. Every time there was a fast transition, assist was gone. I assume this was because I was moving the box piston faster then the pump could flow. What I'd like to try to understand is if this is a lack of flow symptom, or a warn out, 55 year old, steering box issue which now has a lot of internal bypass going on in the control servo valve.

I don't have enough experience with PS box's to understand if this is a common thing, and I don't have the flow number on a factory pump vs my pump to know if I'm way off etc. I can rock the the wheel side to side and easily find the limits with the current setup, I'm really hoping it's the box.... I don't have a factory pump to put on there anyway to test. (magnum swapped car), but I may just have to try that before replacing the box.

When I got the car, it was being driven with no pump on a power box, so I have no idea if the box worked well then, it alwasy just had lots of play until I put the electric pump on it.

Thanks all for your thoughts.