I'm in GA with much the same weather. I question how much good encapsulation does without actually heating and cooling the encapsulated space. There's no way you could recoup the cost of installing one, even if you did the labor yourself. You'd be much better off replacing the ductwork for the HVAC, any way you can ride it out and time it to coincide with replacing the HVAC unit?

You can try sealing seams in the plastic, and then sealing to tot eh foundation. Fastening to the foundation usually the harder part. I have used various 'plastic' boards (including ones designed for decks) fastened to the inside of the foundation with siliconized latex caulk behind the boards to seal there. The plastic is then sealed to the face of the board. If you use deck width boards you can usually rip them at least in half, and sometimes narrower if you then treat them gently.

I just helped my friend who owns a cabin in the mountains which has a basement that one wall is at 50% undergrade and the other exposed wall, cinder block. Since mold comes from dirt 100% vapor barrier is crucially important to slowing down mold spores in the air. Though mold is everywhere exposed ground that does not receive mold killing UV sunlight grows uncontrolled. I would suggest never to put wood on top of the plastic because it will wick moisture considerably and rot. I reccomend slab pavers and float them next to each other. https://www.google.com/search?q=4+x4+ft+cement+pavers&sxsrf=ALeKk02V51mbSbLGF1xq4pOhQ9u3cpq95A:1599487146944&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjqnt35mdfrAhWnlXIEHUgkBq4Q_AUoAnoECA0QBA&biw=1366&bih=657#imgrc=dIckdvbXW2X8QM Better choice pour a 4 inch floor but thats usually too costly. Get www.SensorPush.com ($50) Humidity device with gateway ($100) which will always show you your rooms humidity level. If not conditioning with AC that pushes 50% humidity air to keep air dry you would want fans that evaporate moisture. The biggest concern are critters...mice..chewing electric wires, in furniture...etc. Get www.MouseX.com to drive them away but not kill them so there dying in the walls of your home. I would REALLY stray away from spun insulation above head. Mice nest in this CONSIDERABLY then snakes hunt them as the snakes push and pull your insulation as seen in your pictures. Mice can chew through steel, concrete block and wood easily and any plastic...so the goal is to not give them a easy nesting place. Mice have really made some thouroughfairs in the header joists to previously get into the room. But no mold means no camel crickets or cockroaches which mice eat, no mice means no snakes. So lower humidity so wood beams are under 16% wood moisture content and they wont grow mold and shuts down thebentire food chain. Snakes enter the space from digging under the foundation and coming up right next to the foundation so sealing the plastic to the walls slows the critters down. Sealing the plastic is done best with pin nails shot from a .23 caliber pin nail gun NO MORE than 16 inches apart that keeps the plastic tight enough to keep out snakes. Keep the mice out keeps the snakes out. On top of the 3x3ft or 4x4 ft cement pavers you could put interlocking 3/4 in foam boards and cover with carpet or throw rugs. My friends neighbor works at Trane and got a DEEEAL on central air system system. : )

Just to make a huge clarification - "encapsulation" is the process of closing off a crawlspace to the outside air, closing off the floor to moisture, insulating the walls, and air sealing. You are essentially making this unoccupied area a part of the house, just as you do a basement. Whether you add a "mud slab" (thin, non-structural concrete floor) on top of the vapor retarder is inconsequential to the act of "encapsulation." Your contractor has gone above and beyond (apparently unsolicited from you) for a crawlspace by installing footing drain tile, damp proofing, and a dimpled membrane. That was an excellent decision and gives a hint of the level of house you may be building. So since you have paid extra for that, and now have a properly drained foundation, IMO it would make sense to pay additional ($4K on a $500K home?) for a mud slab to match that level of build. It is not required to seal off the floor from moisture, but provides good "housekeeping" (easy to clean & keep clean) for the crawlspace. You will have HVAC there, be accessing it, and probably store some things too. Nuts/bolts and other comments: - Just as FYI, 2" of gravel doesn't really do much. It won't really compact well (nor does #57 do so to begin with), which is contrary to what you need when under a concrete slab. If you are doing 2" thick concrete, then the slab will be harder to float smooth as the 1" size of minimally-compacted stone will jut under the vapor retarder, creating little pockets into the 2" concrete thickness, so potentially your slab may not look as smooth as a patio, and you may get some cracks over the thinner areas. With 3" there is more concrete cover and the slab should perform and look better. Typically a gravel base is 4" thick, max 3/4" size. The differences aren't critical for a crawlspace, but just giving this info in case you have preferences for how your crawlspace looks and can evaluate the cost choices you have. - What you do have with the gravel layer is a drainage plane. As a bonus, this allows good movement of radon gas. Even in the SE, like Georgia, radon is prevalent. It makes sense now, for very little cost, to install corrugated pipe around the perimeter of the crawlspace. Provide a stub up through the concrete to allow you to connect to it in the future.