Do the Perfectwater folks have a plan for getting it hooked up? That one is an RO faucet, nicely geared for hooking up with John Guest, but may be a little tricky getting from what appears to be a 7/16-24 UNS (1/4" compression) male threaded stem to your 3/8" BSP softener without going via JG

Awesome, I am glad you made progress. Let us know if it works!