Fascinating. Whilst the square search was taught at Nav School and we considered it once it was not as easy as it first appears.
We soon found that at narrow track spacing we needed to use the modified square search to allow for the turn radius so we effectively searched boxes 1 - 3 - 5 then 2 -4 -6 and so on.
Then time was hugely significant. With a track spacing of 5 miles and not allowing for a turning circle the first box would, IIRC, be 60 miles. At 3 miles per minute that was about 20 minutes. Box 2 was 135 miles. Box 3 was 215 miles and into serious search time - if my rusty fag packet is correct.
The other refinement was to fly the planned headings on each leg not correcting for wind but to calculate the mean wind during the search at the end of the search by taking a fix and measuring the error between the DR position at the end of the search.
Post flight analysis would then me applied to plot out the actual ground covered so that a second or subsequent search patter could cover any areas missed.