Flat drying and then rows is what we used to do for stacking too. But baling, that needs a machine, right?
Wikimedia seems to have a list of haystack images by country at https://commons.wikimedia.org/wiki/Category:Haystacks_by_cou... and what do you know, Swiss actually do it differently! Building around a central pole, rather than a more elaborate frame https://commons.wikimedia.org/wiki/Category:Haystacks_in_Swi...