I do indeed know when the Spanish American War took place. I also know that contemporary photos mostly show the troops with officially sanction fore and aft folds to the crown, not in the later, Montana Peak style. There's fairly famous photo of Roosevelt and his Rough Riders, all wearing 1889 pattern campaign hats. Of the maybe thirty or so figures in the photo maybe four have blocked their hats into the Mountie/Montana/ Boy Scout style.
Pretty much all the photos of US troops in the Philippines and China Expedition, both roughly contemporaneous to the Boer War, show US troops, both Army and Marines with their campaign hats blocked in the official fore and aft style. If there was a variation in those were generally that the front and or rear was folded or pinned up, a bit like Corporal O'Rourke in F Troop.
bI also know that the official adoption of that style was not adopted in US dress manuals until about a decade later.
I'm not suggesting that it wasn't worn unofficially by individuals. clearly it was, as were other sometimes bizarre individual variations. The point I'm making is that the period evidence of the four square lemon squeezer style is pretty much limited to individuals.