So... For me, here is what I've tried...
I uninstalled Intel RST and reinitialized the new SSD after copying off all the data. Then I got version 15.7 of the AHCI drivers from
this link and installed them without installing the RST application. Then I was able to copy all the files back and the drive remained at SATA/600. However, something I have been unable to identify seems to be causing it to revert to SATA/300 again.
Weird.