As I understand it, the NEC only allows a complete listed assembly to be operated at 100% of its rating. This would mean not just the circuit breaker, but all of the attached components, devices and conductors would have to be tested together and listed as an assembly. This is probably not something that you can design and put together on your own without a field visit from UL.
Take a look at the wording in the first sentence of [NEC 2011] 210.19[A],1, Exception regarding branch circuit conductor ratings and then 210.20[A], Exception regarding overcurrent protection device ratings. They are exactly the same with regard to listed assemblies rated for operation at 100% of their rating.
It looks that according to 210.20[A], a circuit breaker would normally be sized for 100% of the non-continuous load, plus 125% of the continuous load, just like branch circuit conductors.
So, if in this case you have a 19A calculated continuous load, then it appears that both the circuit breaker and branch circuit conductors would need to be sized for 19A X 125%= 23.75A.
Since #12 conductors for all temperature ratings in Table 310.15[B],16 are limited to a 20A maximum OCP by 240.4[D],5 it seems you basically have two choices. Reduce the continuous load on the circuit or increase the size of the circuit breaker to 25A and the conductors to #10.
IMO, in this situation the 25A rating for #12 in table 310.15[B], 16 would not help because the circuit breaker also has to be considered, but also IMO, when you get into #12 being used as a neutral conductor where OCP is not involved, then that is when the 25A rating can sometimes come into play.
