I see absolutely NO MENTION of 5w-30 dino oil being remotely close to acceptable for this application
You're right, I don't know how I got it in my mind that the OP's Bimmer was a '94 and and not an '04 but I did.
Anyway BMW's viscosity reserves in there spec' oils are substantial. Running a somewhat lighter 30 grade synthetic oil in reality is not much lighter than the spec' BMW 5W-30 in service (I haven't seen a UOA that hasn't sheared at least 10% even after as little as a 1,000 miles). And BMW doesn't specify anything heavier even for track use which in my experience raises the viscosity requirements by at least 0.3-0.4cP HTHS.
And for what it's worth BMW Canada is on record stating any premium synthetic can be used once the vehicle is out of warranty.
BMW started specifying in 2005 their LL-01 FE 0W-30 (HTHSV 3.0cP) for the M54 sucessor, the N51 as an option.
So for a strictly street driven 325Ci with the M54 engine, I contend that any 5W-30 synthetic will more than satisfy the viscosity requirements of the engine.