Under the vehicle, you will see four holes pressed in the floor, from memory something like 3" x 4", there are removable panels from inside the vehicle that are only held in by a thin metallic tab, all four of mine have rusted through and have left the panel to move up and down freely, easiest way to check is to simply poke the panel with your finger and see if it lifts from the underside. I have to pull my interior next summer and weld them shut. Never saw the purpose of them in the first place. This may or may not be your problem but can be easily fixed if so when you have the carpet out.
You will most likely have to pull the front seats, centre console and the rear seat bottom, rear seat bottom is easiest as it is held in place by two clips, pushing straight backwards by the bottom of the seat and pushing up slightly does it. You only have to move the seat 1/2 to 3/4" in backwards to free it from the clips. When drying the jute sound material, separate it from the carpet, if possible spread the carpet out flat, it will make it go back a whole lot easier than if you drape it over something, They tend to take the shape of whatever they are bent over. All in all good luck and I hope your floor is not too bad under all that water.