I spent a lot of time trying to accomplish this with a Wildcat MK1 in .177.
The FX reg in that gun would not go that low in stock configuration. Rather than play with the washer stack, I ordered a HUMA. I did get the Huma down to 12fpe with reasonably consistent speeds. However, the best I could get on target was a one inch group at 25 yards. Earnest said if I sent it in, the reg, hammer, spring and other tuning should get me the equivalent of a UK spec Non-FAC gun. I don't doubt him BUT, since I was doing pretty well over the chrony, I just couldn't get past my belief that the barre l(at least the one in my gun) just wouldn't shoot at the lower speeds. So the cost of custom tuning and a new selected barrel just didn't seem worth it to me. Taking that same gun and increasing the speeds back to about 19 fpe made it shoot just fine, it was better at 23fpe but that wasn't something I was interested in.
Different gun, and was really just an experiment, I actually have a .22 Impact tuned to shoot 12fpe for driveway plinking this winter. Not really what I want an impact for and it will be retuned to higher power again as soon as I find something more appropriate.... Still really hoping to fids a way to get a 12fpe UK Spec Wildcat.