Good Morning

Depending on the size of the pit we will put a piece of Lexan on the pit seal it down drill our holes for the piping and wires and install a dranjer valve. Sometimes will we will use the solid sump pump cover doing the same thing and then we add a site glass to the lid, or use the new clear some covers. Put a label on in it stating that it is part of the radon reduction system.
We have had very few problems doing them this way.

Good morning: we also use the lexan method we buy it from a sheet supplier and get them to cut it into 2' X 4' sheets for us so it easily fits onto truck and reduces cost significantly from buying from big box stores. One of my guys was having trouble sourcing lexan locally and has gone to checker plate aluminium does it ever look sharp!

Ditto for the Lexan. Seal to floor with silicone, which can be removed easily.

I've sometimes fastened a cover with removable concrete anchors and used soft rubber tubing as a gasket between the cover and the concrete, run around the perimeter of the hole.

I guess I wasn't clear in my description of the problem. We've also always used 1/4" Lexan for sump covers. We've also been able to buy 4'x8' sheets locally and cut them into 2'x4' pieces and we've used all the techniques for sealing that you have all described depending on the surface we need to seal down to. My concern is with the rare, but problematic, issue where the "sump hole" is a 6" to 1' dug out depression in the floor with a pedestal sump pump just sitting in the hole. I suspect it's there not so much for water table problems but for dealing with surface water and I don't want to eliminate it.

For something that small, I would probably line the pit with mortar or concrete.

We had a similar situation. We used a crawlspace sump pit from RCI, which is smaller than a standard sump pit. We had enlarge the hole somewhat to accommodate it. We replaced the pedestal pump with a submersable and installed a Dranger drain in the lid so water could drain down through the lid.
We also used the refurbished pit for our suction point.

We typically cover non-standard sump pits with Lexan. We mount a 6x6 PVC utility drain (no bell trap) with an 1-1/2" PVC trap mounted to the underside of the cover Often a hand dug pit is located at the low spot where water would puddle. An 1-1/2" drain will handle large amounts of water without clogging. I would caution against sealing or lining the pit with concrete. Sometime the water problem that inspired the pit was a result of ground water or hydro-static pressure. Sealing the soil may cause the water to find a new entry point resulting in a water problem that you created. The best option would be to install a perforated liner with a Lexan cover and floor drain.

If there is a pedestal sump pump, I give the owner the choice of replacing it with a submersible sump pump before we arrive or paying us to replace it at the time of installation.