440 head noise. Perpetual problems. Problem solved

The heat riser in the exhaust is on the passenger side right below where all the cylinders come together in the exhaust manifold.
If you do have manifolds check to see if there is a stud or a stud with a weight on it going crossways through the manifold just above the pipe flange.
Of course this only applies to cast iron manifolds, so if you have headers it doesn't apply.

See the thing is, there are really only three things that ring like any sort of bell on a motor.
Loose or cracked flex plate.
Heat riser butterfly
Loose pipe to manifold flange

The amount of time you say it takes to start doing it also sounds like it's exhaust heat related.
This is why I am so insistent about the heat riser (or loose manifold to pipe flange)