Possible replacement for the A/C

I just took apart an old window unit I had.The control section its the only part that wound have to be sealed.I think that I would mount them in a waterproof electrical box.

I would just mount them in a plastic case inside the camper and run the wires out

My concern, perhaps already addressed: Can this unit/system handle the vibration, etc. from road travel, in the short & long term? It appears to be designed for static installations. Just a thought...

Has anyone noticed the the vent under the bathroom door? To my knowledge, it doesn't actually serve a purpose (other than access and possibly keeping that space somewhat conditioned?). I wonder if there would be a way to run a duct from a unit mounted on the tongue, under the dinette in the storage space, (assuming yours in the front like mine), and to this vent? Seems like a pretty clean install, and the only thing left to figure out would be how to remove the controls from the unit on the tongue and mount them in the interior.

That vent helps to remove any moisture, and to prevent freeze-ups in cold weather.  I've thought about cutting a hole in the floor under there and mounting a biscuit fan, to push fresh air into the cabin during boondocking trips.  Without A/C you have to leave the windows (and vent) cracked to prevent moisture buildup but that is difficult when it rains.  No reason you couldn't do the same for an A/C like you said.  I would use that as the air return and put the cold air output somewhere else, up high.  Maybe use a removeable hose attached to something that would let you use one of the front windows.  That would eliminate the need to make a hole in the exterior where it is visible, so if you sell in the future you could remove the whole thing and you would never know.