I can't see side clearance being a major cause of clacking.

What procedure did you use to set the valves? Whenever I set hydraulics this is how I do it:

1) get the appropriate lifter on the base circle
2) back off the nut and adjuster so the pushrod has slop
3) turn the pushrod with one hand while tightening the adjuster - when the pushrod stops turning you are at ZERO preload.
4) set the recommended preload ( X turns of the adjuster) and tighten the nut
5) repeat for each lifter