Carbon build up/gunk in the oil pathways to the intake Solenoid/nonreturn check valve

[striker2021]

Hi guys,
Due to the 2A82/87 errors and a few other relevant ones, I replaced both Vanos Solenoids, their filter (non-return check valves), esscentric camshaft position sensor, all coils, all spark plugs. The Vanos solenoids seemed dirty, but their filter (checkvalves) were in horrible shape. Due to previous owners lack of proper maintenance the engine has heavy carbon build up. After these replacements, the engine ran well for about a month, huge boost in power, but recently it throws persistently the 2A82 code (intake Vanos Solenoid jammed). Given that all these are basically new, I am thinking that the oil pathways upstream to the intake solenoid and its filter still has a lot of gunk and carbon build up which quickly saturates and clogs the filters restricting oil flow and pressure to the intake Solenoid. I am about to pull out both solenoids and their check valves (filters), inspect and clean, if they are gunky it points to blocked upstream pathways as a high likelihood culprit.
Question: does anybody know if there is a way to clean or improve the oil pathways upstream to the intake vanos solenoid so that its filter (check valves) doesnt get gunked up so fast? needless to say since I owned the car (3 years ago) I have done oil and filter change every 6K miles, quality OEM filters, and Castrol fully synthetic 5w30 oil. What I am dealing with is the previous owner's mess. Any tips are appreciated. Thanks in advance.

[shogun]

model and model year please, then we will move the thread to the proper model sub forum

[Bmw4life12]

Brother, I have owned numerous e46 and e39 cars. Most of them have had 29+ error codes.
After can or 2 of seafoam, codes no more. Tested dozens of times