Actually when going really slow (first gear just above idle), you want to lean out of the turn. This essentially places most of the rear axle weight on the outside tire, and will help you turn at low speeds. Try it out. Don't be afraid, just ride within your limits and you will get comfortable. Normally at speed, lean into the turns. In wet grass, try to spin the rear end out a bit - like drifting. When riding high powered machines, I find myself steering with the rears almost all the time. Also, when turning, don't just lean into the turn, but move forward. You said you have bike experience, so pretend you are going into a turn hard to rail it, and lean forward as well.
Hope that helps.
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