Well, bud, here is what I would do…
Find a spot in the basement where you can make a plenum for your unit. Then, measure the width of the unit, (w) and the height to the unit (h). Now, measure the depth (d).
Decide what you want to use to make the plenum. Plywood is an option, (it is probably what I would use) but for light weight, maybe galvanized sheet metal is the way to go. It does not matter. Make your plenum box 1” wider and ½” taller than the dehu unit (inside dimension). Make it about 4” on each side deeper (so 8” deeper in total). Coming out of the front, get a section of solid 4” dryer duct (galv sheet metal) and install it in the front of the plenum, so it seals around the edges, using a sealant like silicon caulk. Cut a 4” hole in the intake and exhaust plenum sides. Cut about 1” laterally up the duct pipe in 6 places, evenly spaced around the circumference of the duct, so you create tabs. Slide the duct pipe into the plenum holes until the ends of the cuts line up with the inside face of the plenum. Bend the tabs out, and secure in place with sheet metal screws. Now apply the silicon caulk around the outside of the duct to seal the seam.
Do the same thing with the dryer duct on the back (exhaust) side of the plenum. You should have about 4” of dryer duct protruding from the plenum on each side.
Now, screw the bottom and sides of the plenum together, so you have a box with no lid. Put a bead of silicon on the connecting edges to seal the plenum totally. You don’t want it to leak outside air in, or you will have cold air coming from the vent. Set the unit into the box, and check to see how you are going to secure it to the box. My guess is the unit has feet on it of some sort. Hopefully, they screw in. If they do, then drill holes in the bottom of the box where the feet are, and get longer screws to securely screw the unit to the bottom of the box. You should open the drain cock on the unit permanently, then run a clear hose to the edge of the plenum, and install another drain cock on the outside of the plenum, to be able to drain it when it fills up. Make sure any holes are sealed with silicon. Before securing the unit, put two beads of expanding foam sealant across the bottom of the box, to seal the intake from the exhaust side. Once you screw the unit into place, you can run two beads of expanding foam sealant up each side of it, to seal the sides to the box. The foam will expand and fill the area between the unit and the box completely so that you do not have leaks. Now, run a couple beads across the top of the unit, and secure the top (making sure to silicon the edges of it, too) . The unit should now be completely concealed inside the plenum now, which should look like a plywood box only slightly bigger than the dehu unit with 4” dryer ducts going into and out of it.
Test the unit (you remembered to drill a hole for the cord and then seal it up, right?
Make sure air flows into and out of the plenum freely.
Now, the difficult and scary part. If it were my 5th wheel, the way I would do it is to find two areas in the floor or in a cabinet, over the top of the area I decide to keep the plenum and unit in the basement, where people cannot step. This includes under a table, under a cabinet lip, under a chair, or whatever. The only requirements would be that the air can flow freely around it, and they are far enough apart that the circulation created by them would actually circulate most of the air inside the camper. Then, I would drill 4” holes, and put vent covers (available at your RV store) that match the existing vent covers for my 5th wheel. If you decide to go with in the cabinet, then a hole through the floor and through the cabinet wall will be necessary. Make sure any holes are sealed well once the ducting is routed, to make sure you do not have cold air leaks.
The other option is to find your return air intake, and tie into it with the intake end of your plenum, and then run the exhaust end of your plenum to a heat supply duct. I think you can get solid wye connections for the 4” dryer-duct type ducting used in these campers. Just run your flex duct from the intake plenum to the return air duct, wye into it. Then run your exhaust to a heat supply duct, and wye into it.
Whichever way you go, you will also want to wire up a switch to turn the unit on and off. You can probably find a place to do this inside the camper in a place that is easily accessible.
I know this is a big and complicated set of instructions, but if you go this way, it is the best way (IMHO) to do it and make it a permanent, professional installation, which will use your existing unit, and only cost you $30 to $50 bucks, tops. Once you secure the plenum in the basement, you will never have to think about it again.
The only thing that I did not look into is if the unit needs periodic cleaning. If so, then it may be advisable to use foam rubber seals around the unit, and a hinged top, so it can be removed for cleaning. The foam rubber seals will not seal as well, but they will do the job.
I could not find any info on the supply/return ducts for your camper, but my guess is that with a little searching, you can find out sizes/fitting needed to connect the plenum to the ducts. Also, if your basement is not insulated and heated, then you need to worry about duct insulation, and also insulating the unit, so the water does not freeze inside of it and the clear drain hose.
This is what I would do, but I also have a pension for making things too complicated because my Dad always told me to “do it right or don’t do it at all”.
My way makes it so you don’t have to buy a new dehu unit, and it will only cost $30 to $50 bucks (did I already say that?) Anyway, maybe I am on crack and it isn’t a good way to do it, but it is what I would try…
Good luck