If you live in an area it freezes, the second option is contraindicated. The condensate in the system will freeze inside the pipe and block it. It takes up as much room as a 3" or 4" pipe if exposed, or a small wall bumpout (vertical bulkhead) to hide it. It does not take up much space in the interior, and if you need an active system, the fan is installed in the attic. In retrofits, where a system is installed in an older home, it is often run through a closet, out of sight. Any active system should have vibrations mitigated to stop noise transfer in the house. Passive system does not have this problem.

Once you landscape, you should solve most of your water problem. Adding exterior water proofing and drain tile around the entire foundation to exit on the down hill side will solve the rest of the intrusion into the crawl space.There really are no shortcuts in dealing with active water intrusion into a crawl/basement space. Preventing the water from entering is really the only sure way to maintain a dry space. As for the radon abatement, there are lots of solutions. Passive abatement is the least expensive long term. That means installing a grid of drain tiles(holes downward) and a stand pipe(extending to a height above the roof) under gravel. Then the plastic you mentioned and pour the concrete floor. The passive system is done without the concrete, with the plastic sheeting glued to the foundation walls and any pipes. Pouring a floor over it is fine., but the sealing is still very important, as concrete alone will not effectively seal against the gas. Which is forced from the earth naturally by pressure in the earth. Even though radon is heavier than air, the passive system does not allow the gas anywhere to go save into the piping and eventually up the stand pipe and out into the outside.

"it's typically to install gravel and perforated piping under a slab connected to a continuously operating fan to minimize the potential for radon to enter the structure. Implementing that at this point would involve cutting and excavating the concrete slab." "If those aren't currently in place, the OP is back to an excavation project." Tim, I try to avoid these internet tit-for-tats. But it boils down to this: Your comments put in the OP's head that they have to remove the slab and install a loop of perforated piping in a gravel base. That is not true and not ever a practical option. Apparently you aren't aware of the common method of extraction points. And that's ok. It doesn't negate your obvious intelligence or reduce your extensive experience. Rather than trying to back out of a hole with what you said by parsing words and playing which cup is the ball under, sometimes it's just better to admit you weren't familiar with that system for retrofitting existing homes. I've been wrong before and have misread or haven't thought of things in threads before too. I either correct myself, re-evaluate my answer with new info, or move on, but I don't worry about saving face.

I di not hear mine at all inside and only if i put my ear to the unit outside do I hear it. I often think it might not be working.