I have a 12 35i 185k, almost identical issues.

The water pump “waking up” and other shadow codes were definitely that water pump. The oil sensor, water pump, alternator, battery management (IBS) all share a serial bus interface wire ( think party line). When one component fails and pulls the bus wire down, the other items either can’t communicate or start doing funny things until the failed component is fixed. In this case, the most likely is the water pump because the electronics are all housed within the case where coolant eventually leaks.

Here’s what I have done to “save” this e70. The thing was a steal so I wasn’t too worried about spending the money on parts. I started with what I knew to be broken or overdue and later just started throwing parts at it.

-Valve cover- ruptured diaphragm and rotten valves within the valve cover
-Valvetronic motor (I did this while I had the valve cover off. I DO NOT recommend this unless you’re prepared to replace the eccentric shaft, bearings, etc at the same time. The shaft wears a pattern into the bearings and gears wear a pattern into each other. Once disturbed, valvetronic motor current sensing is too sensitive and a run in cannot be done. Ask me how I know)
-Plugs and coils (Delphi)
-Intake Vanos solenoid- present code
-Intake valve cleaning, intake gaskets (including the gasket for the DME), sealing rings on charge pipes, cleaned maf
-A/F sensor- just because
-Injectors and coded them- shot in the dark. The plugs were pretty darkened and at 184k, I figured why not.
-Cleaned exhaust Vanos solenoid
-Oil filler cap gasket- any air leakage into the crankcase is a vacuum leak. The valve cover is a very integral part of the intake system, to this engine’s detriment.
-Reset adaptations each time something major is done.
-Battery (Age)

I’ve gotten to the point that I’ll live with it for now until something actually breaks. It’s strong at WOT like the op’s and it’s just partial throttle where I feel a mild bucking sensation. I grabbed Carly to see some live data that I couldn’t see on other tools but I haven’t had an ah-ha moment. High pressure fuel reading looks fairly normal, throttle input, advance/retard of cams, MAP and MAF readings..

OP- a new thing I have noticed is that at night with the dome/map lights on, I can see some flickering from the lights that seem to be influenced by the engine operation and speed. Do you notice anything like that?