The bit about Tonmeister/Balance Engineer in the guideline you link to is weird. As you point out, there is a relationship type for just that, and there it says:
Balance engineers typically have additional music engineering experience specific to the extra demands of classical music.
This relationship should also be used for Tonmeister credits.
This relationship type should only be used if the engineering credit
specifies a balance engineer role. In case of conflicting engineering
types (for example “Tonmeister / Recording Engineer / Ingénieur du son /
Ingegnere del suono”), use just "engineer".
The relationship style guideline is probably just out of date, but it would be interesting to hear more from people more involved in style issues.
I would probably just use producer for recording producer. I've edited a lot of Deutsche Grammophon releases in the past, but I can't remember what I'd chosen then. I wouldn't be surprised if I alternated between producer and recorded by in the past, because it's such an edge case.