The title sort of covers the question. The GS6-53 shifter carrier is completely than the Getrag 420 carrier.
Who has done this swap, and how did you resolved this?
Wouldn't the linkage from 330i ZHP (GS6-37BZ) work? It uses also uses a dual-ear carrier.
'99 Estoril Blue + Dove Grey ///M3 coupe
'04 Jet Black + Cinnamon ///M3 coupe
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