The character was made in the 1940s and as such has an intrinsic connection to that era. His motivations were stated and even the styles used for him. The trappings scream of the era, not the 80s. You endlessly refuse to see this and as such are avoiding it as it takes down your argument.
Considering some of the absurdities of 80's fashion, Starman's costume wouldn't be too much of a problem.
The fin could probably be explained away as somehow.
That is not a sliding timeline, it's moving them. Superman, Batman and Wonder Woman are three DC examples of sliding timelines. They never stopped being published and were always re-iterated for the era they were in. The JSA have not and would not be. Given the thread here being on Marvel, in comparison it's no different then with Superman and crew. You cannot move characters from the 1940s to the 1980s and then call it a sliding timeline. For it to be one, it would be from the 40s to now with the backgrounds rebuilt up. The big difference is that with Marvel, most of the characters are still more contemporary than the JSA. What you're saying does not work, it does not bring any sort of equilibrium, it creates an anachronism.
Will you please stop being hooked on the 80's? I'm talking about placing the JSA's starting point in a period of time 20-30 years from the JLA's ever-present "now". The particular decade doesn't matter that way, at it will always be 30 years from the "present."
The JSA exist in normal time. The JLA exists in sliding time. The JSA were founded in 1940, the JLA was founded (let's say) 5-10 years from an ever-present now. The JSA ages normally (juryrigged things like slowed metabolisms and limbo notwithstanding). The JLA doesn't age.
The absurdity of this just gets worse as time goes on, if you wanted the two teams interacting with each other on a regular basis.
As said, you want the modern heroes to have mentors? Use character from the era you site instead of moving the originals. Also, what you get is a weakened modern version. Either leave the JSA in the 40s and go multigenerational as Byrne did with Generations, sans the apocryphal stories, and build it to there. Otherwise leave it as is now.
Why is it weakened? The JSA would be strengthened by living "outside" of time like the JLA does. They woudn't be getting older and older like they are now.