Yes, 12 feet is too short for 12 gal with 65F tap water.
I would suggest making post-chiller submerged in ice water, recirculate wort until it falls to 100F (at the end of CFC) and then pass it trough ice water.
I have 25 feet CFC and it takes 45-60 minutes to chill 10 gallons to 63F with 61F tap water.
Since I have HERMS, at my last batch I used HEX as post chiller- I filled it with ice and added water just to cover ice. I passed wort to HEX after it drops to 100F and it took ~20 minutes to run whole 10 gal batch cooled to 60F.