Is this the m54 or one of the v8s? It's not uncommon on the six cylinder cars to see injector 5 in particular develop a leak. Did you ever hear any pops or backfires of sorts in your exhaust. If it were me I would probably swap injector 2 and 5 see what happens. Or just do the whole bank.

I replaced my o2s at first when dealing with lean codes but I don't think they really go bad. It was due to vacuum leaks from the disa and the caps for that pump on the back of the intake manifold. But that was lean codes. For too rich I like what you're thinking with injectors. It could also be the maf.

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'05 E53 3.0 6mt
'17 F30 340ix 6mt
'96 E36 328is, in progress