Genghis,
Just my little piece, (oh err)
Anyways, the gliding fraternity avoid standard square circuits like the plague because the last thing you want is to fly a downwind, away from your landing area only to turn base and find you are no longer in gliding distance of your field. They have adapted the circuit to include a 45 degree leg between the latter stages of downwind and base. The result is that they are always within gliding distance of their target field.
I have taken this over to my powered flying, I just wish I had variable airbrakes.
Any instructor who forces students to fly a standard circuit pattern is setting them up for trouble IMHO.
The other technique I am practicing at the moment is as you describe with a constant sight picture and varying the turn on a long curved approach from downwind onto final.
As my instructor said time and again, keep sight of your field and never turn your back on it.
Obs cop