It sounds like your tappets are a different shape to what the were originally, as they have "mushroomed" from being continuously banged on the head and this causes poorer lubrication and the noise you are hearing. Nothing you can do to stop this from happening, it happens with these lifters.
Replacing the oil with some quality synthetic stuff might help you if they are not too bad, otherwise, try some engine flush (ask a decent mechanic about that) as it gets rid of the gunk in there (sometimes), but you don't drive around on it (as you probably are aware NZ).
Shims should work, but a better solution is to replace the lifters with new ones. This is hard to do yourself, unless you have the right tool, and is a bit costly to pay for. My advice, try the engine/oil flush if the noise really gets to you, but use quality oil from now on (btw you should always use quality oil regardless of what condition the engine is in).