Hi there,
I'm not a spinning expert but want to reply to refresh your question.
I'd highly recommend watching a couple of old Troutboynz videos on YouTube of spin fishing with small Rapala lures (look like tiny brown trout).
They did very well. As you say, cast at 3 o'clock, twitching/winding back across and down.
Mepps spinners are legendary, so probably also worth a go. Just don't get sold a lure that's meant for trolling, not casting.
I used to do very well using another spinning method - small ball sinker with a leader to a smelt style fly, in the Waikato region.
again, casting up and across, letting it drift and a quick retrieve at the end.
A silver Rabbit fly is deadly in that situation (I was fishing to trout that were zeroed in on smelt). But an Olive Woolly Bugger would also be a good choice.
You'd just need to adapt the sinker weight to suit your local river. I used to use a quarter or half ounce ball sinker, and about 8lb fluorocarbon leader. But that was in heavy, rough water. In those days i used mono main line, but modern fishing is probably done with braid.