Ferenginar would actually be interesting, provided it comes with more stuff to do with latinum besides waste it on holo emitters.
I'm picturing some kind of stock market like investment minigame, a latinum store with various consumables and permanent costume items that also pay you latinum for items you sell to them, and the ability to hire Ferengi privateers for "treasure hunt" missions that work similar to doff assignments, the more you pay the better the quality of the privateers and the better their success chances.
I think Ferenginar would work nicely with a rep system and with repurposing latinum.
My honest preference would be 1969 Earth, tying in with the moon landing but also with preventing time travelers from ending the space program (ie. cancelling Star Trek). What better year for the fate of Star Trek to hang in the balance than the year TOS was cancelled?
You can riff on the Mad Men vibe while it's still somewhat popular. If you think about it, there are dozens of characters from Trek active in that era, particularly when you consider that anyone who showed up in the 30s, 40s, 50s, and 60s in Trek could be active in that era. So you could have a bookstore selling Bennie Russell books, a U.S. Government where the Air Force knows a little about Ferengi, Gary Seven running around, Dixon Hill novels in print or maybe a Dixon Hill film at the movie theater, the very beginning of Chronowerx Industries. There are a zillion logos from the IP that could be in use and it would be wild to have Thomas "Mad Men" them up. Maybe an ancestor of Buck Bokai or Zefram Cochrane or that guy who flirted with Jadzia.
It's also a wild enough time that aliens could pass for mods or hippies.
And here's the big one: Redjac was hosted by a Soviet at that point. So you could totally get away with making him a Bond villain and with no likeness issues to worry about.
Also, it could crack me up to have "dollar bills" as a reputation currency akin to "Romulan marks." So you'd make it this whole "Go out and collect the weird green paper that the natives seem to value to advance." Y'Know, sell some antique eyeglasses, steal some clothes, maybe knock over a crooked mob run business and loot the register.