The well company came out to do the sealing and backfilling. The floor of the hole below was covered with cement, then bentonite, further limiting water penetration immediately adjacent to the well casing.
The outcome of the work seems hopeful at this point: the water is looking decent, although there haven't been any heavy downpours since the job was done. I did a follow-up qualitative bacterial test (the quantitative one from UGA costs over forty dollars, so I'm satisfied with qualitative for the moment).
I used one of the Industrial Test Systems coliform tests. The culture medium, when dissolved in the sample, makes it look like a urine test. If no coliform bacteria are present, that's how it will stay.
If, on the other hand, coliform bacteria are present, it will turn blue-green. Above is how the sample looked at 24 hours, sitting on the kitchen counter at about 79-80 degrees.
Later, it became pretty obvious. The label further notes that in the presence of
Escherichia coli, aka E. coli, the sample will fluoresce blue when an ultraviolet (365 nm) light is shone through it.
It looked pretty fluorescent and blue to me; E. coli it was. So this was disappointing but not necessarily unexpected. I did shock the well with chlorine bleach in June after the first test, but there had been rain since then that had silted everything up--so a new influx of bacteria-contaminated water was almost expected. Alas.
I also got new measurements on the well (24 inches in diameter, about 16 feet of water at the bottom, equaling roughly 375 gallons; see: this calculator...basically, the volume in cubic inches or feet can be estimated using pi x r squared x height, then divided by 231 cubic inches or 0.1337cubic feet per gallon [7.48 gallons per cubic foot]).
UGA and other sites recommend adding enough bleach to get to about 200 ppm of free chlorine; I used 6% bleach so adjusted my amount accordingly and added about 1.5 gallons, diluted with water before pouring it in so I wouldn't risk damaging pump wiring or anything else). See also this guide from Canada.
I then ran the bleachy water through the whole system, into the pressure tank, water heater, and out every fixture in the house (of which there are not many--kitchen and bathroom sinks, toilet, tub/shower). I returned the next day and started pulling chlorinated water out of the well. UGA and everyone else recommends, "Rid the system of the remaining chlorine by turning on outside faucets, one at a time, and letting them run until you no longer smell chlorine." That's easier said than done. There's some concern about dumping heavily-chlorinated water on plants and in my case, we're talking 375 gallons (although some at the bottom is inaccessible because it's below the level of the pump).
So far, I haven't seen any indication of plant trouble, but I have only poured water on grass. Mostly I have run it into a stock tank for 24 hours to let the chlorine dissipate, then poured it out.
So the well seems to be fixed. I've also flushed out a lot of sediment from the pressure tank and water heater that got in there before the reno; hopefully all I'll have to deal with now is a little sand here and there. The purple vial above is the coliform culture from the First Alert water testing kit (ITS also sells one that looks pretty similar). It started off and remained purple; it turns yellow in the presence of coliforms. That's mildly encouraging. While I wouldn't expect any bacteria in the well at this point, I drew the sample from the kitchen faucet, so it shows I successfully got chlorine throughout the system. Now it should stay negative. A subsequent follow-up was still negative, which was more encouraging. Now there are just the lingering silt issues...below is what's coming out of the tap after passing through a one micron nominal filter.