AHCI mode must be selected before install of the OS. Trying to change to AHCI mode after installation will not work. I am not sure if this is applicable to your situation as its not clear which disc is the boot disc.
Also running in mixed mode doesn't really work. So the best solution is to do a fresh install on the SSD after setting AHCI mode in BIOS. And yes, I would move the SSD to the SATA III 0 channel.