While Superman & Batman played such negligible roles in the original JSA comics, their removal has never really been much of a problem following the merging of Earth-1 and Earth-2. However, Wonder Woman played a pretty major role in enough of them that keeping her out of the JSA has always been an issue.
Given the popularity of the WW1-set movie, the best solution to me would be to establish that, at some point early in her superhero career, Diana was thrown back in time where she secretly fought in various historical settings ranging from the Trojan War with Achilles & Hector, in Camelot against Morgana LeFay, alongside Mulan against the Hun invasions in China, the Napoleonic Wars, WW1 and WW2, where she joined the Justice Society for a few years, before being returning to the present day, having retroactively added a centuries long legend of a "Wonder Woman" who had appeared at various key moments in history.
This would also let DC have its cake and eat it by keeping Wonder Woman's origin and her first meeting with Steve Trevor in the present day, while also allowing her a vast history that spans the history of the DCU--or just the 1940s if they don't want to mess around too much. Replacing the Golden Age Wonder Woman with Hippolyta was an interesting notion, but it ended up diminishing Diana's importance within the DCU by making her a precursor to her own mother, who often ended up being a more interesting character because she wasn't saddled with Perez's virginal stick up her butt characterization.
If DC doesn't want to do this, they have three other options from what I can see if they want to keep the JSA on the same Earth as the modern age superheroes.
A) Leave Wonder Woman's spot on the JSA empty, like they did with Superman & Batman. It leaves the JSA essentially a men's club until Black Canary joins in '47, but it doesn't change much. I think this probably the least interesting choice.
B) Fill Wonder Woman's spot with another established character like they did Post-Crisis with Miss America and Fury. Personally, I think neither of these characters work for me because they simply aren't Wonder Woman-esque enough to really fit the bill. Even Fury, who was created by Roy Thomas to be a replacement for the Golden Age Wonder Woman, is too visually distinct from the classic Amazing Amazon archetype.
C) Create a new Wonder Woman-type heroine to take her place called "Suprema". She could be visually similar to the early Wonder Woman, but different enough from the modern version to not cause too much confusion. She could be an Earth girl raised on the alien planet Zamaron by its immortal female rulers in the ways of love and granted extraordinary abilities during her time with them. Suprema could, of course, heroically sacrifice herself to save the JSA prior to 1950 or simply head back to Zamaron.
Granted, option C has some of the dangers of the Hippolyta retcon, but since Suprema's "Wonder Woman" moniker would only be used similar to how Superman is referred to as the "Man of Steel" or Batman as the "Caped Crusader", Diana wouldn't be viewed as a legacy character or subordinate to her Golden Age counterpart.
Does anyone have any other options that DON'T involve separating the DCU back into Earth-1 and Earth-2 again? I agree that's a very simply solution, but I don't think it's the angle that DC is planning on taking with the JSA once they return.