Old Hercules & later Alliant handloaders manua;s gave the length of 1 oz of shot in the various. They did not stipulate the shot hardness or size. I am going to stick my neck out a bit & assume it was ordinary chilled shot of a size around 7 to 8 as these are sizes loades by a lot of target shooters for which reloading has been quite popular.
The column length for 1oz in the 16 gauge was .837". A 16 is .662" in diameter, give or take a bit of manufacturing tolerance.
Quite obviously the 1 oz load did not give superior results in you 16 because it was Square, because it is in fact (.837/.662 = 1.264 ) 26%+ OUT OF SQUARE.
About the only loads which have ever been factory loaded close to square are 1 1/16 oz in 12ga & 1 oz in 10 ga.
The 3/4 oz load in a 28 gauge which is so highly touted as having Near Magical abilities has a length of around 220% its diameter. 1.212L/.550D
Even the oz load in a .410 is 266% times its diameter. 1oz = 2.18" 2 for oz =1.09. 1.09/.41 = 2.6585
These are of course subject to small variations due to actual alloy &/or shot size.
I cannot truly say if I ever shot an actual Square Load in my life. As long as I picked a reasonable load & shot size for the game at hand & THEN POINTED THE GUN IN THE RIGHT DIRECTION I never had a problem with those Skewed Out of Square loads killing anything.
A square load in the 10 is actually 1.27oz ( would be a bit lighter with larger size shot normally associated with the 10), a 12 = 1.0565oz (close aplenty to 1 1/16oz), the 16 = .790oz (25/32+), the 20 = .634oz (5/8+), the 28 = .455oz (7/16+ & the .410 = .189oz (3/16oz).
There are your Square loads, how many folks you reckon shoot them??