Hi Peter, anything i say here is coming from pretty limited river fishing so take my answer as a theory starting point!
You've got the idea right in the sense of what you're trying to do is place slack line in areas where the current is detrimental to what you're trying. For example if you were casting straight across and the middle of the stream had a fast current, you'd cast across then move the rod tip upstream, shoot line some line, and return rod to centre. You'd then have a mend of line upstream creating a bow to delay drag on the fly. That's a reach cast but the names aren't important.
There are honestly a million different ways of creating slack line. Some of these have actual cast names and you could do much worse than by reading some of this:
Sexyloops Flycasting Contents If you scroll down you'll see "presentation casts". As you are doing, wiggling the tip - take that a step further and think of where you want you're wiggles or slack. The tip will do whatever you want to do to the line. Move the rod tip to the side immediately after stopping and you'll get a wave travelling down to the end of the line. Delay it and you can make it much nearer the rod. Experiment with it and see if you can solve the problem. Try the casts mentioned on sexyloops. And let us know how you get on

Or if you can, get along to an instructor or a casting club near you and ask for a demonstration/advice!