I finally bit the bullet and purchased a new set of wheels for Baby.

Based on suggestions and comments from many of you out there, I decided on a set of "M Parallel Spoke 37" wheels for her, moving from the 16-inch OE wheels to 18's.

Problem was that BMW only sold this style in the "M" version, making them about the most expensive wheel I saw in their entire catalog...for any car. $2800 for a set of four: 2 front, 2 rear.
Even with a BMWCCA "discount" from my local dealer, I was looking at something like $2300...they said they might be able to do the set for ~$1800...,but even that was still kinda high for my budget...just for the wheels.

However, one of the experts at the dealer told me they'd been seeing some Excellent knockoffs of this particular wheel in the marketplace...they show up on cars that come into their shop and the service folks said they were very impressed with the quality of the clone wheels. The dealer expert said I might want to look for those knockoffs...price would certainly be less.
After checking on this and another on-line source for E38 owners, I found that many fellow 740 owners had purchased replica M-parallel wheels from Wheel Exchange in North Carolina. After a year of waiting, I finally ordered my set, shod with new Michelin Pilot Sport A/S tires.

I'm very pleased with the results! The wheels and tires are "staggered" on Baby -- meaning I have 9.5-inch width on the rear and 8-inch on the front, just as they come set up from BMW on the 740 "Sport" models..Listed below are the BMW part numbers for the wheels I wanted, and for which I found perfect replicas, for just $800 for the set.

BMW OE PART Number SIZE
37 11 2 227 631 (front) 8 x 18
37 11 2 227 633 (rear) 9.5 x 18

All four replica wheels, with new tires mounted, spin balanced, with metal stem covers, BMW Roundel and M-series inserts installed, lug nuts, etc., were only about $1900 total, delivered to my front door.
The wheels went on very easily, not a hitch...they're hub-centric, so no spacers, etc. Yes, I realize they're about 2-3 pounds heavier (each) than the BMW M-parallels, but for the difference in cost, I'm very happy.