Based on the information you have provided, the problem(s) you are experiencing are all related to the camshaft system. I say that because of two of the three DTCs you are getting (P1345 and P0014). Also, the P0420 DTC (catalytic convertor efficiency is below threshold) could also be the result of the problem with the camshaft system.
If you have not already done so, go ahead and replace the VVT solenoid. While you are at it, look at the electrical connector that plugs into the VVT solenoid. Make sure the wires are intact,and that the side that goes into the VVT solenoid is clean. If it is not clean, use some rubbing alcohol to clean it.
Now, find the camshaft position sensor and look over the wires going to it. Make sure the wires are intact going into the connector body itself. Remove the connector from the camshaft position sensor and make sure the part that goes into the sensor is clean. If not, clean it using some rubbing alcohol.
If any of the wires going into the VVT Solenoid or the camshaft position sensor are loose, broken, etc, then you'll need to get a replacement connector and splice it in place of the old connector.
OK, now clear the codes and drive around and see if either the P1345 or P0014 codes return. If either code comes back, I would then replace the camshaft position sensor. They do go bad from time to time.
If only the P0420 code remains, drive the TrailBlazer on the highway to see if it stays or goes away. If it goes away, then you are all set. If the P0420 code is still there, remove the the Oxygen sensor that is before the catalytic convertor (it's mounted in the exhaust manifold) secure the loose Oxygen sensor and then drive around and see if the engine runs better and is no longer sluggish. If the sluggishness is gone, you have a catalytic converter that is partially plugged and will only get worse, so it will need to be replaced.
If the sluggishness is still present, please report back for more guidance.
Either way, please let us know how it is going.
