I would suggest trying cotton stock style 5394-Pantheralla. this is 85% cotton and 15% Nylon. Which give for a thicker sock. While the style you do not like is is 65% Cotton Isle and 15% Nylon which makes for a thinner sock.
But I do suggest possibly trying a different brand when it comes to the elasticity because all of Pantherella is anywhere from 15%-35% Nylon which will give it the elastic feel you do not like. style 14435 Falke
is 60% Wool, 23% Cotton, 15% Polyamide, 2% Elastane. This will give you the thicker sock and also less elasticity.
Richard from Lake Forest, Il/USA