Sandman, it is true that you will finally catch up to the flipped sail as you continue to turn but successful gybing takes a bit more input from the rider. If your board is balanced as you say, you are probably dropping close to the water at the end as you have lost too much speed. Speed during a gybe is your friend, your foil is much more stable at speed. That's why most people advise to gybe on a gust. When you go into the turn oversheet and lay down the sail a bit (not full on like a pro) this will help keep some speed up and turn a bit tighter in the first part of the gybe. The aim should be to keep power in the sail as long as possible and to get power on as soon as you can. It's a very fine line to know when to flip though.
Going into a gybe from a downwind run can be very different from going up wind into a gybe though.

The gybes above were mostly from off the wind. Going a fair bit faster than the windspeed it is so easy to get backwinded. In this situation I only oversheet momentarily as I enter the gybe before the flip. You may need to help the sail around the first part of the flip with the backhand. Then just try and keep everything as smooth as possible until you can catch the sail. Because I am still going faster than the windspeed at this point there is very little power in the sail. I try to fly out of these quite high so I can drop down on the foil to create a bit of acceleration. Once you have a bit of power back in the sail head back to a reach or up wind.

A lot of these gybes are up wind to up wind which I find a lot less technical. Because going up wind I am only going a similar speed to the wind the chance of being backwinded is far less. I can stay oversheeted a bit longer and carve a bit harder and when I flip, the sail comes round much quicker. Also because I am probably going slower than the wind speed the sail is powered up as soon as I catch it.
The only way to learn is go out and do it again and again and again. Forget long runs of foiling bliss for a while and just gybe. You will be surprised how quickly you get it. I wish I had done it 12 months before I did. The drifting round waiting for things to come to you like many of us have done will get you so far but you have to make it happen.
Can you spot my crash on the tracks?