340 is knocking
was getting louder as it was warming up more.
I think we can rule out the idea of an exhaust leak, as they usually disappear or quite significantly as the motor warms(materials expand and contract with heat and cold). What is the oil pressure readings as all of this is going on? What does the gauge read when its warmed up?
With the noise intensifying after being warmed up, the thinning of the oil seems to be aggitating the noise. This could be a noisy rocker(loose hold down) or maybe the oiling holes on the shafts are facing the wrong direction? A lifter may be noisier if the oil thins, but I have always had them quiet sown with warmth.
On the bottom end, the intensified noise when warm could be a signature of a rod bearing issue. Again, what is the oil pressure when warm? I had a bad wrist pin in a motor once that had symptoms similar to what you have described.
All and all, valvetrain or rotating assembly, the thinning of oil with a warm engine is playing a part in whatever this is.