It is important to slide as in a Vulcan. Aim to pop the board around exactly 180 degrees. Aiming farther than that will make you very likely to land on your heels and fall backwards. As with so many moves, keep your weight as far towards the nose as possible during the entire move. You need to be farther forward than for a Vulcan.
Landing with the mast next to your hip will make things difficult, so try especially hard to get the mast across your body and to windward early, like before you land. (Watch my video to see me do this wrong. I still pull if off by doing extra well on the next part.)
Make the rotation happen by pushing the mast even farther into the wind, not at all toward the tail of the board. If you are falling over your toes as the mast goes down with you then pull less across the board and more toward the nose at the start.
Do not consciously try to flip the sail. It will happen by itself. It is extra important to not push on the clew hand. This will kill everything.
If you go too much downwind then you'll probably end up with a Spock 540, which is cool, but if you're really going for the 360 it helps to be close to a beam reach. As you go more downwind the sail becomes less likely to flip by itself (get ripped from your clew hand).