Thanks for the response, Doug, and sorry for the late acknowledgement. A bunch of other issues came up regarding this monitor and I've been going back and forth with vendors for days trying to understand and solve problems.
The POST/BIOS screens refuse to appear on this BenQ monitor, so I can't get into BIOS. But when I add the old monitor as a secondary display and boot, the POST/BIOS screens appear there. Turns out there is some issue between the newer UFEI boot control and the old BIOS boot control. Looks like I will have to convert my older "MBR" system disk to UEFI, which looks like a complicated process.
But to your comment, the saturation shift when I toggle the monitor between Adobe98 and sRGB is static. If does not change when I "touch" the image inside Photoshop. In Windows Color Management I started with only 1 profile, the "BenQ SW270C Color Profile,D6500". So I added sRGB and Adobe98 profiles and set them as defaults to test. Neither one made any difference.
Another issue is that the "Factory Calibrated" BenQ is supposed to include a printed calibration report. Mine had none. Nothing in the box but a quick start guide showing how to assemble. I queried BenQ support, and several days later I received an e-mail with a PDF calibration report. Even though the report shows my serial number, I'm a little suspicious. In the meantime, I challenged B&H about this. They quickly offered to replace the monitor, but refused to open boxes to see if calibration reports are included in any. I asked them to just loan me a profiler, but they said no can do. Finally, their rep said just order one, use it, and return it. So that's what I've done.