I would give a last list of characters, but they are actually mash up of characters from Smallville (some which can be traced to previous works or comics, not everyone is from Smallville and some are not mash ups)
Team Arrow (give Black Canary true sonic attack)
Team Flash (With Jesse Quick an honorary member and the Liberty Bell powers besides her speed)
1.Andrea Rojas (plus Cassandra Carver, plus Ryan James but also Jordan Cross, besides foreseeing death could foresee other things, and Kevin Grady, no blindness but capability to fight blindfolded and night vision, and Sara Conroy, and Alec Abrams),
2.Arthur Curry
3.Batman (only if he comes from another universe, it has been stablish he does not exist in the arrowverse but comes over from somewhere else),
4.Bette Sans Souci, reformed (plus Wesley Dodds, plus Kyle Tippet, through the helmet of Nabu a heir to Kent Nelson)
5.Chloe Sullivan analogue (brainiac like intelligence, truth compeling, healing)
6.Cyrus Krupp (mixed with Maddie Van Horn)
7.Hawkgirl (no Hawkman, the actor's horse face was nause-inducing),
8.Jayna,
9.John Henry Irons; Steel (similar to Victor Stone, yet not the same and with such a backstory that despite there being no superman in the arrowverse he still exists as we know him)
10.Obsidian,
11.Resurrection Man
12.Swamp Thing
13.Zan and
14.Zatanna Zatara

The JSA is better when they don't have to live in the shadow of the trinity
Don't agree but you have a point.
On Jay Garrick's Earth, they JSA should be him
As I have said.
Robert Queen's Green Arrow
Why not that Earth's Oliver Queen?
Dinah Drake's Black Canary,
Sure.
Alan Scott (Call him Sentinel if we still can't say GL)
As I have said and call him Green Lantern. If he cannot be Green Lantern have Stargirl with her Cosmic Rod instead.
Star Spangled Kid (Retired) Stripey (Active as STRIPE)
Wrong, wrong.
Stargirl,
Again only if we cannot have Green Lantern.
Obsidian, Jade, Atom Smasher, and Damage.
All wrong. You need Carter Hall/Hawkman.
If you do not want the trinity you have instead as you say Dinah Drake/Black Canary, Rex Tyler/Hourman, Wesley Dodds/ the Sandman.

The JSA is better when they don't have to live in the shadow of the trinity.
On Jay Garrick's Earth, they JSA should be him, Robert Queen's Green Arrow, Dinah Drake's Black Canary, Alan Scott (Call him Sentinel if we still can't say GL) Star Spangled Kid (Retired) Stripey (Active as STRIPE) Stargirl, Obsidian, Jade, Atom Smasher, and Damage.
They all strive to deviate from the norm, but collectively swarm to be all the same.