Those flexible vent runs, if filled with water are going to sag even farther into the belly. For the most part those are un-supported and run thru the framework. I am guessing your going to have to open up the coroplast and drain those ducts from underneath.
My suggestion is to open the bottom of the trailer up and disconnect the ductwork from the furnace and let hang down and drain. It’s not likely that you can reach every nook and cranny with a ShopVac and the residual water may generate odors of its own when the furnace runs. Once drained, use a blower at the high end of each run to evaporate any residual moisture.
Be careful with the ductwork, it’s whisper thin and won’t take a lot of muscling about.
I am in the process of redoing my duct work and several other items after squirrels got in and ate holes in several ducts. The 4 inch ducts are run along the sides and through the frame. there is a lot of room to move around in the belly. There is no easy way that I know of to rerun the duct without dropping the cerroplast bottom.
You might try tying a string to the duct where it attaches to the floor register and then disconnecting it from the register. If you're really lucky, the water will drain out of the duct, into the underbelly. Use the string to retrieve the duct and reattach to the register. If the water drained into the underbelly, drill a few 1/4" holes in the coroplast to let the water drain onto the ground. The coroplast is at most 1/4" thick, so don't drill more than that so you don't contact anything else.
If you don't want to drop the entire underbelly, you could cut a flap just big enough for you to get inside. That's what I did when I figured out the factory never screwed my shower P-trap together. Just leave the hinge side of the flap towards the front of the trailer so the wind won't catch it while driving. I just used eternabond tape to reseal everything once I was done. The greywater pipe was directly in my way to completely drop the coroplast in that area, which is why I decided to just make a hole. There are wires just laying on top of the coroplast, so use a razor blade, and go shallow and slow.