'Can this be done without removing the water and the fish?'
In a word, no. At least not easily or effectively.
Rinse the Flourite outside and have it ready.
Put your fish in a bucket. Siphon off 30 - 50% of the water (if possible) into another bucket. Then siphon off the rest of the water, down to the substrate.
Pull all the substrate and now you are left with about 1 - 1.5" of black, gunky water in the bottom of the empty tank.
Hopefully you have enough Flourite for a depth of 3" or 4" (slope from 1.5"-front; to 3" - 4"-back).
Dump in the flourite right over top of the gunk. It will cover it and your bio-colony is left in tact(no need to recycle). Lay a bowl on the flourite you just put in and 'leveled' out. Re-fill by pouring your saved tank water into the bowl and letting it
SLOWLY fill the bowl and then
gently overflow the bowl and fill the tank.
Leave the bowl in as long as you think it will deter the re-fill water from stirring up the substrate.
Now you still have the water that the fish are in and fresh water to add back. Just add back your water very slowly until the tank is full again.
Plant the tank and there you go!!!! Very simple.
This can be accomplished in 10 - 30 minutes. The fish will not even miss a beat. They will think you just performed a large water change and love you for it.

Just keep your water temps., fresh and old. reasonably uniform and use your dechlorinater for the new water.
Len