Big field here. I'm not sure you have a KE problem, but if you did I would expect a big air leak. Its not likely to be fuel pressure as it would have no reason to improve with full throttle.
It could easily be secondary ignition. The problem can occur two ways. One is that at a certain required voltage the spark finds a lower resistant path to ground shunting the needed spark. The rotor is a common cause of this type event. The second way is that available voltage is reduced (by a bad coil) causing a threshold where required voltage exceeds the current capabilities.
The reason either of these events can fit your senario is that idling is a minimum voltage requirement. Low rpm loading is probably the highest voltage requirement, which drops as timing increases and load is reduced with higher rpms.
Plugged cats probably fall under the same concept as fuel pressure: they shouldn't improve with rpm.
KE electronic control could go wild (not likely) and can be eliminated from consideration by just unplugging the EHA connection after warmed up. Car should run just fine with The EHA unplugged when warm.
Bosch Master, ASE Master, L1
33 years MB technician