the rpms do happen slower in third and you are running higher rpms longer...so ur correct about that.
now onto the pump. It's not really about the pump keeping up with how FAST it revs. Its mainly about putting the volume out for as long as it needs to put it out. Since you're at higher rpms longer in third, the pump has to constantly flow a HUGE volume of fuel. If the pump is on its way out...it just can't flow that huge volume of fuel for as long as it needs to.
It may be able to hold up for a little while in the higher rpms, but it seems that his pump just can't hold up for the amount of time he's at the top end of third. My bet is that if he was to floor it in fourth gear he'd be having problems at a bit lower of an rpm since it accelerates even slower in fourth and requires even more fuel to overcome wind resistance, drag, etc.....that'd be at a rather dangerous speed though.
Just trying to help you see what's going on. Hope I didn't make things more confusing for you....I have a habit of doing that lol.
someone feel free to chime in if my logic seems a bit wrong