Your premise may be central to your story. But that doesn't mean that it requires paragraphs of explanation, or that you should sideline the characters and just talk about your awesome idea. Rather, if you find that the explication of your idea is taking too much time, you probably just aren't cutting it hard enough.
To illustrate, let me post the first three paragraphs from the query letter from a novel I completed last year:
Haris is an Apostle, a first-contact specialist dedicated to renewing
ties with forgotten human colonies. He arrives in secret on the planet
Hesychia disguised as a native, leaving his high-tech home to live
among the crippled beggars, silk-swaddled nobles, and stern monks of
the low-tech world. His mission is to integrate himself into their
society and convince them to rejoin the interstellar community. But
nothing goes as planned.
Two different religious factions pursue him from the moment he
arrives, and he finds himself betrayed and sold into slavery. In
captivity he meets Layra, a slave girl who claims to be his wife and
knows everything about his mission. Haris cannot understand how
everyone he meets seems to know him already, but Layra explains to him
the astounding truth: on Hesychia everyone remembers the future.
Some who remember Haris support his goals, while others are out to
hinder and kill him. With Layra's help Haris must find out which are
which---if he can even trust her. And though Layra remembers that
Haris ultimately succeeds, Haris discovers that memory can deceive.
(The omitted fourth paragraph has the title, wordcount, and boring biographical details.)
I'm posting this, not because I think I have the awesomest query ever, but because I faced many of the same problems that you are facing. The setting is complex, as the book contains both an advanced space-faring society traveling from world to world, and a low-tech society that the protag visits. On the low-tech world I have to allude to the problems of the class and religious structure, including multiple religious and political factions, and somehow get across the idea of how all of these connect to the central idea of the story, which is a society built around a shared memory of the future.
How do I get all of this into the query letter? Mostly by leaving nearly everything out. I mention exactly two central characters, never mentioning the antagonist or the supporting cast at all. The POV character of the first chapter never even appears! Almost all of the setting is compressed into a single sentence in the first paragraph. And the exciting central premise is relegated to the second paragraph, with most of its implications left to the reader's imagination. It's okay to leave things unexplained in the query letter, so long as you can entice the reader to keep looking, and convince them that you have answers in the full MS.
I happen to have a paperback copy of Hyperion on the bookshelf behind me, so let's look at its back cover copy. (A common querying technique is to pretend that you're writing the back cover copy.) How does it present the premise and characters?
On the world called Hyperion, beyond the law of the Hegemony of Man,
there waits the creature called the Shrike. There are those who
worship it. There are those who fear it. And there are those who have
vowed to destroy it. In the Valley of the Time Tombs, where huge,
brooding structures move backward through time, the Shrike waits for
them all. On the eve of Armageddon with the entire galaxy at war,
seven pilgrims set forth on a final voyage to Hyperion seeking the
answers to the unsolved riddles of their lives. Each carries a
desperate hope--and a terrible secret. And one may hold the fate of
humanity in his hands.
This copy presents the Shrike as the main character, which is an interesting choice since the Shrike is arguably the antagonist. But this works because there is no one protagonist in Hyperion, but all seven main characters have the same antagonist. Furthermore, we very quickly get exactly what Reid recommends: the situation (mysterious creature on a backwater planet), the plot (seven people coming to supplicate/confront him), and the stakes (fate of the galaxy). None of the seven protags gets named. The setting is almost completely omitted. The cruciform parasite, which is arguably the most important idea of the series, never shows up either. It's all boiled down to the absolute minimum.
So it can be done. For your novel, peel away the layers of complexity that you've lovingly arranged and get down to the bone. Figure out what the most interesting and most important thing is. Present that. Leave everything else out.