Have you thought of an exhaust manifold leak; it has all the symptoms.
The vast majority of small manifold leaks pop when cold under acceleration, then seal up when hot.
Maybe leaking around the EGR system, if your car has one, or the manifold is cracked.
If the tick only occurs during acceleration, and not when just revving in neutral, it seems unlikely to be a valvetrain issue to me. The valvetrain and the oil supply don't know whether you are accelerating wide open or in neutral.

But..... covering all the bases; the hydraulic actuators (valve lifters) can be replaced relatively easily and inexpensively. They are in the ends of the rocker arms, so teardown is very minimal.

DG