I doubt it's the hammer spring if 2 barrels don't do it and one does. If you put the "working" barrels back on since trying the 223 barrel, do they work still?
If so, I'm betting it's a locking lug issue on your 223 barrel. Try polishing the barrel lugs or another set of lugs off your other barrels. If the other lugs make it work, call TC and have them send you a set of locking lugs for the 223.