Hmmmm.... if I'm reading your post correctly it seems like you are confusing a couple of different types of gybes (some sort of longboard sink or pivot gybe (from Jem Hall) and a regular carve gybe on a shortboard (weight forward...room for the body..rig forward.. drive the board round).
If I remeber correctly you have a large Carve, right?
OK, the longboard pivot/sink gybe isn't going to work very well on your Carve, but you can do something similar on your Carve board, just don't step back so far, don't sink the tail so much, and put the rig well out on the windward side of the board and the power in the sail will drive you around. This sort of gybe works when you are "slogging.
It can be referred to as a flare gybe.
If you have a bit more speed, then a flare gybe will still work is if you aren't powered up completely, but if you arr planing along you can turn it into a "flarve" gybe.
This gybe combines the elements of a non-planing flare gybe and a carve gybe.
You take your back foot out of the strap before you enter, and place it over near the lee rail (and a bit forward, but behind the front footstrap) .
Apply some pressure on that back foot to "tip the board" downwind to start your gybe.
At the same time, bring your rig across the board and ut the mast well upwind to steer the board around to downwind.
When your are nearly downwind, flip your sail, then power it up on the new tack.
When you switch your feet can be as you work your way around, or later after the board is on the new course.
When you have lots of wind, you can go for a fully carving gybe.
So at what point in your gybe attempts do you tend to fall in most often.
Hope this helps,