Number one, your well guy is offering a short term solution at best and is thinking about his pocket more than your health.
Number two, your casing as Boyce said should be higher. Standard of the industry domestic casing is called 6” but it’s actually 65/8 diameter.
Number three, I’ve had the best luck pulling the water level way down in the well before adding the chlorine, I want a high chlorine level. Then run a hose from the house to the well and let the water circulate for about 30 minutes washing down the casing, drop pipe and wire. Then install the cap and pull the chlorine through the entire system, faucets, tubs,showers, spigots, washing machine, dishwasher and the humidifier if you have one. Let the chlorine sit over night and start running it off the next day.
Number four, when the chlorine is gone wait a week then resample. Take the water to a certified lab that same day. Forget a mail order water analysis, I’ve seen too many that give false results.