What's the point of setting it in the Star Trek universe if you aren't going to use elements from the Star Trek universe?
Last I checked the universe is pretty big. You don't need different people(or different actors) doing the same things over, just slightly differently. Not if you're trying to tell a story that hasn't been done before. You say TOS is your favorite series, well it was them going after new things. Isn't that what you want from a future things instead of a rehash of the TOS days?
You can tie in to existing plot elements without blatantly ripping them off too. Doing a tribble episode just to do a tribble episode is fairly pointless as it's been done before. We don't need to be reminded that tribbles put rabbits to shame in breeding and don't like Klingons and coo soothingly. We know that already, another episode about it is redundant.