I thought I would post a follow-up on this.
Apparently the only way to be able to use new HDDs that have the PWDIS feature enabled on pin 3 with older power supplies, is to prevent the HDD from getting 3.3V on pin 3. There seems to be 2 approaches to doing this in situations where those older power supplies are compliant with SATA specs prior to 3.2+:
1. Use a molex to SATA adapter, since 3.3V will not be provided for pins 1-3.
2. Use Kapton self-adhesive 1 mil tape to tape over pin 3 (taping over pins 1-3 also works, just be sure that all of pin 3 is covered).
Since my server connects all of the HDDs through a backplane (power supplied via molex connectors) with built-in SATA power and is fully compliant with the SATA power specs, my only options are:
1. Buy a new server case that has a backplane compliant with the new spec.
2. Use option 2 above.
Although I have not ruled out option 1 (new case) completely, I have proceeded with option 2, and I am pleased to report that even as I am writing this reply, the server is resilvering the "taped" drive.
Status is: RESOLVED!!
Big thanks to all that have provided input that pointed me in the right direction.:D