Hi Phil, sorry for the slow reply; I missed this somehow.

Did your question mean to change the 14 AWG to 12 AWG and leave it on a 15Amp breaker?
Or do you mean, run a new 12 AWG circuit with a 20 Amp breaker?
The first scenario wouldn't get him much, the breaker would still trip. (though the OP hasn't tried it yet. I don't think it will trip, as long as nothing else is on that circuit)
The whole new 12 AWG on a 20 Amp circuit is a good idea. If that's what you mean.
I ran two 20 Amp circuits to my HT. Alonf with the original 15 Amp circuit.
I posted what I did earlier, just so the OP wouldn't change his 15 Amp breaker with a 20 and leave it on the 14 AWG underrated wire. That's a code violation.
Regards,
Rick