Peter Saroney at Armalon is, of course, still cutting up new No4 Mk2s to make his .223/5.56mm carbine thingys. You might be able to get a barrel from him.

Nearly every .223 conversion I've come across (mostly the above-mentioned Armalons), the owners have complained about all sorts of feeding and functioning problems. Maybe the geometry of the No4 feed-ramp to chamber is simply not optimum for a thin round?