First off, I think you’ve still got an EGR problem of some kind. Not saying that’s the cause of the high speed sputtering, but it could be. You say your idle is not so good, and that’s likely due to the EGR problem remaining. Replacing the valve wouldn’t fix an EGR problem that was caused by the control system telling the valve to open when in fact it shouldn’t. A constricted vacuum hose could cause that to happen, among other things. EGR systems during that era were quite complicated. There’s usually multiple electronic controlled vacuum switches involved with the control function, as well as temperate sensors.
For the high speed sputtering problem, assuming all the routine engine maintenance is up to date according to the owner’s manual schedule, especially fuel filter, engine air filter, and spark plugs, I’d start by reading out all the stored diagnostic codes and go from there. A partially plugged cat should be considered too.
You are mostly correct. The fuel pressure is held constant independent of engine rpm, and the amount of fuel injected depends only on the duration of time the injector is pulsed open. High fuel demands result in a higher % of time the injectors are pulsed open. The actual fuel pressure at the rail (if you measured it referenced to ambient air pressure) does vary a little with engine load b/c the pressure that affects fuel flow is the difference between the fuel rail and the intake manifold. So when the intake manifold vacuum level is high (low pressure), the fuel rail pressure will be a little lower, and when the intake manifold vacuum is low (near ambient air pressure), the fuel rail pressure will be a little higher to compensate.