How you sell a JSA centered continuum is acknowledging there have been Batman and Superman movies already. Acknowledge that Batman has been established in the “present” with Keaton/Kilmer/Clooney and certainly acknowledge Christopher Reeves as Superman. This saves you from having to establish them in the timeline, especially as both have had their origin story told before.
Also, by having established locations like Gotham City, Metropolis, Smallville, and the like means that you can play off of that knowledge and fill in the DC map. Where is Star City for the Star Man movie? If Keystone City is in Pennsylvania, is it analogous to Pittsburgh or Philadelphia? This will not only flesh out the “DCEU”, but will mean if/when the “current” iteration of the Flash or Green Lantern arrives, then fans would know where they would fit in both chronologically and geographically.