I would sanitize the well and plumbing system. I suggest
http://www.moravecwaterwells.com/index.php/maintainance/disinfection-and-testing as a more effective but doable for DIY. I would bypass the water softener during part but not all of the sanitizing. Do your initial water recirculation via an outside hose tap. Once the recirculated water is up to high levels, I would feed water through the internal plumbing and run water so that each faucet is putting out 50 ppm or greater. This includes hot water. Run hot and cold water into the washing machine too.
Keep circulating the well water through the casing. Look to the web page for times, but longer won't hurt.
If your casing is large enough, you can drop some of your chlorine down the casing pellets made for the purpose. The advantage is they sink to the bottom and hit the area below the circulation. I have a 4 inch casing with a 3.75 inch pump, so I could not drop the 3/8 inch pellets to the bottom. I used liquid chlorine bleach and hth brand "shock 'n swim" #3 (calcium hypochlorite 47.8%) granules, which is sold for pools. The granules are much smaller than the well pellets, but I hoped some of the granules
might make it past my pump that is set down 140 ft. I compensated for not getting pellets to the bottom by circulating much longer. Once the circulation water is at high level chlorine, wash the sides of the casing and the pitless.
I would get some high-range chlorine test paper such as Hydrion Cm-240 Chlorine 10-200 PPM.
Consider some narrower range pH test paper such as Hydrion (O67) Urine & Saliva pH Paper 5.5-8.0. I found that it took a few seconds to get the color I expected rather than the right color being instantaneous. I did not test against standard solution however. The range is low enough to tell if you have added enough vinegar, and it is high enough to check common pH levels after the well has been purged of the chemicals. You can get by without the test papers, but I think it greatly improves the confidence that you have the right levels even reaching through the water heater to the faucets.
To hold my flooding level water as described in the procedure, I used a 33 gallon garbage clean, but I lined it with 2 layers of large can liners. I filled that with the high-level chlorine water circulating, and then covered that with a third can liner bag. When I put the flooding volume in the next day, I used a clean 1/2 inch vinyl hose that I had as a siphon. I soaked the hose in the chlorine solution to make sure it was sterile too. I got my casing levels and flooding volume to have over 200 ppm. Better overkill than underkill in this case.
I chose to put a big inline filter in the hose line that I was recirculating back to the casing. I already had the filter. It was not only to remove any solids, it was a way to see if anything was captured. If I did not have the spare BB housing, I probably would not have done that otherwise.
With septic, I minimized how much chlorine solution I put down the drains to the septic tank. It can accept some. But once I got the levels I wanted, I stopped the flow and let inside faucets and valves sit. On the inside stuff, I thinks I drained the WH to minimize dilution. Weaker chlorine plus time can do a good job of disinfecting. The higher levels I had in the well I dumped into a ditch with a garden hose.
How to get there right amount of chlorine but not too much into your water softener resin is something that I don't have a clear procedure for. It should get some, but less than other things. I have ideas on that.
