e53 2002 misfire over 4000rpm or high speeds

[ne0beatsm0rp98]

Hey everyone, new member so hi

Anyway i have a 2002 e53 petrol automatic.
If i floor it over 3,500-4000 rpm the engine management light comes on and the car shudders with low power. If i stop and restart engine it goes back to normal but obviously same issue arises if i go abover 3,5000rpm.
Also on motorways even if i stay below 3,5000rpm and say i hit 70mph and hit a slight incline the engine management light comes on and same issue again, need to pull over and restart car.

On a diagnostic it comes up as 1 & 3 cylinder misfire.

Now its been into a bmw specialist and they had it 2 weeks now. They replaced all the usual, sparks, coil pack, fuel filter, o2 sensors, checked for pressure leaks.

Finally after spending £650 on different jobs to get to this point, there claiming that previous owner has removed the two cats, so if the two cats get refitted at a cost of around £500 it should resolve the issue.

Now im on here because after speaking to numerous other garages, they are claiming it wont resolve the issue as removal of the cats wont cause limp mode as removal of cats increases power which people do all the time.

After reading around, a few different suggestions have come up including the head gasket needing resealing.
So my question is has anyone else come across this issue? If so any ideas on how to repair it or what it could be? Just seems that different places have different views on what it is to repair it.

Thanks