The picture is a little bit blurry so it’s hard to see what the residue looks like. IPA and a brush is usually effective but some times you need to brush over a dust-free wipe, such as a Kimwipe, to actually lift any floating residue. If the carbon residue is “baked-on”, then something stronger may be necessary but you have to be careful what you use as you don’t want to damage or corrode the elements of the logic board. Maybe a chemist can hop onto this thread.
A shop could probably put the board through an ultrasonic bath which would certainly be an improvement. At some point, if the board doesn’t work, the shields should probably be removed for a proper “full” cleaning.