I can do something close, but yet entirely possible within our known sciences.
In 1984, Larry Niven published a book called The Integral Trees. The setting is a vast gas torus, around a neutron star. The gas torus is a known object, and Niven did the math to make the setting scientifically accurate. This gas torus was formed by a gas giant's atmosphere being sucked into orbit around the neutron star.
The gas torus was located 26,000 kilometers away from the neutron star, but, after a detailed examination of the numbers- distances, the neutron star's size, orbit time, etc, it was found that it was incorrect. But by adding a zero to the kilometers, it was corrected. So, Niven just dropped a zero, and removed public interest in this fantastical object.
So we have a place for floating islands, but no floating islands. And that's where Jupiter's Trojans come in. They are two large clusters of asteroids at Jupiter's L4 and L5 points. These asteroids are numerous, and there are estimated to be around 600,000 asteroids in between 2km and 1km in the L4 group. In the L5 group, there are over 1 million asteroids above 1km in size.
Now, we just put these two things together. It is not a world in the strictest sense, but no world seldom is. The main problem is the absence of gravity, but we don't know what happens when someone is born in zero gravity. That means you can make something up for yourself. There is a miniscule amount of gravity on these asteroids, but it's so negligible it could just be called zero gravity. Plants should still be able to grow downwards on their own. They should be extremely tall, but I cannot find anything about that. This should be enough for your world, as anything else would be not be your work.