So the way these acoustic players (phonographs) worked was by having a continuous column of air from the back side of a diaphragm on a 'sound box' that was at the upper end of the 'needle' (yes, needle is the correct term on these, as the stylus did actually resemble a sewing needle) at the end of the tone arm all the way to the opening of the horn. It's the same principle as a megaphone; eventually folks worked out that an exponential flare was best suited to 'accurate' reproduction, rather than a simple conical flare. What this means is the horn was almost always affixed at its base on the rear right corner of the top of the unit, since it had to be able to connect to the tone arm. So from the standpoint of 'accuracy' I would be inclined to flip the horn L/R so it's affixed to the other rear corner of the units.
The large floral style horns were one option, though there were other designs that folded the horn into the cabinet.
Here's a page with a lot more information about these than you could ever reasonably want, and some pictures for reference, if that helps.