I'm new to swimming and downloaded the TI DVD's to self coach. Not sure if the following is of any use to you but...
When you say you have tried "Balance Drills" what do you actually mean?
I'm new to swimming but I plan a pool session of 45 minutes as follows:
1. 15 mins (approx) of superman glide but I don't push off the wall.
I stand in 4 foot of water. Position hands out in front of me under the water surface with my hands submerged under the water, approximately, at waist height. (This will be the same position my hands will be in when I am lying flat on the water, i.e. with my head facing down towards the bottom of the pool I can just catch my thumbs out of the corner of my eyes - I know now head and hands are correctly positioned). I push gently off the bottom, end up horizontal as above and a dolphin flick of the legs just to get my entire body to stretch out. I try maintain this while exhaling slowly from the nose. This can be anywhere from 3 - 7 seconds long. I do this repeatedly but it is in my mind all the time to RELAX.
2. 15 mins (approx) of using off (similar hands as above) wait 2-3 seconds for body to pop up (water pushes me up - buoyancy) to the surface and THEN begin stroking. I stroke with my left arm first and then while the right arm is recovering I try and incorporate a breath. This involves looking at the side of the pool and seeing it. I'll do this on both sides. I continue another 2 strokes to ensure I am full exhaled and then stand up.
3. 15 mins (approx) I now try and incorporate the above efforts into swimming a length. Then I wait 20 - 30 seconds to make sure I'm fresh again and repeat same. Towards the end of this 15 mins I find I am getting less tired and breathless and can do the lengths more comfortably. (I believe this is just that my technique is improving bit by bit)
I found, for myself anyway, I had to be very disciplined and focused. Essentially, not be concerned about what anyone else is doing in the pool, what's going on elsewhere just repeatedly keep trying. I was hard on myself initially but then something just registered that I had to be patient - Rome wasn't built in a day kind of thing. i also found that I had to relook at the DVD's (at least 50 times now) as there was always something I missed!