Obs cop,
Just to clear a matter, pedantic I'm sure, but it is relevant. As a glider pilot I learned always to make the circuit on the downwind side (how rare is a wind straight down the strip?) The point being, and this is the whole point of the constant aspect approach, you can at any time during the circuit, turn in and land with minimal manouvering as close to into wind as the conditions permit.
I had an instructor try to teach me these square thingies; he couldn't do it as well as I could do a constant aspect PFL.
He also reckoned that one should fly a straight line from the high-key to the low key positions (and then a straight base and final).
I have heard only one argument for square circuit PFL's that holds any water. It is so that an engine failure is handled like a normal landing.
I believe if you take a look at the accident statistics you will see that the number of stall/spin/loss of control/poorly judged accidents after such a simple event as an engine failure show this argument to be seriously flawed.