It can backflow if you lose pressure. Perhaps from a power outage, or if you draw water faster than the pump can replenish it.
Backflow valves (check valves) are pretty cheap (about $5 - $10). If the consequences are as severe as you make them out to be, I'd put one in.
Also I would add a carbon filter after the RO system, that would remove ammonia and other things, just in case. If the water was clean the filter would not get worn, so it's cheap insurance that you can leave there for a long time without replacing the filter.
PS. It's good you are not trying to drink softened water - the extra salt is not good for you.
200 yards is a long way when it comes to drilled wells. I'm probably that far downhill of one that is filled to the top, and mine has a static level 100 feet down. Your neighbors may also use water differently than you do.
You appear to be overpumping your well (taking water out faster than it flows in) - You evidently have one piece of data (305 foot depth) but lack many others: depth of pump setting, information about the pump, flow-rate measured at time of drilling the well, static water level, diameter of well - some of those you may be able to gather, or find from the company that drilled the well in the first place.
On your own, you can shut off everything that uses water, wait a while (preferably several hours or more) to let the well fill to the maximum static level, and then fill buckets as fast as possible to try and determine what your effective storage capacity above the pump is. When the well stops, wait an hour and repeat, and THAT will tell you the effective refill rate:
If you pull 200 gallons the first time and 50 gallons the second, you are getting 50 gallons per hour (more or less - since time passes as you fill the buckets) - which is less than one gallon per minute. That can be plenty of water if you don't overdo it (watering the garden can take a LOT of water, depending how you do that - changing to drip irrigation might cut down the rate of use a lot, .vs. sprinklers, say) and have reasonable storage capacity ( in this hypothetical example, the first 200 gallons, or 4 hours with of inflow) to allow for washing, bathtubs, and refilling toilets, etc.
If you require more flow than your well provides and any water conserving measures you are willing to take are not enough, you can have the well worked on by a well-drilling (or well-servicing - often the same, but not always) company in various ways - hydrofracking being perhaps the most trendy (pumping in high-pressure water to open up cracks in the rock to allow water to flow in faster) - unfortunately, it's usually fairly expensive and results are generally not guaranteed.
Best Answer
I have a chlorine injection water treatment system for our well water. The chlorine tank has a dip hose with a filter on the submersed end. This hose runs to an injection pump. There is a dial on the pump for setting the dose to be injected per cycle of the pump, which is triggered by a water flow valve. The injector also has a valve to prevent back-pressure from forcing water into the pump and conceivably into the chlorine tank
But wait, there's more.
The now-chlorine-infused water should then enter a settling tank, to remove reactants from the chlorine and any sediment. The next tank should be a carbon filter to remove left-over chlorine. If you have a water conditioner/softener, that's the next stop on its travel to your plumbing/dispensation within your residence.
It's unlikely that the dip hose filter is clogged.
It's possible a tech turned the dose knob and reduced the volume to zero. There's no set figure for the dose; it's established over time and testing of the chlorine level at the use point.
The injector valve can easily become clogged, especially if you have a high iron content. My valve is called a duckbill and the iron deposits fill the beak, causing it to stick open, allowing more iron into the opening, eventually filling and clogging the valve. Local suppliers will carry the valves, but online is about one-quarter to one-sixth the cost. I believe I paid five dollars each, possibly less for what the locals charge about thirty-five bucks!
After the injection valve, there's very little to go wrong, unless your flow valve is stuck in the off-position. That's very unlikely, as the flow valve would prevent water flow to the house. It's more common to have it stick in the on position, over-dosing the water with chlorine, easily detected by taste and smell.
The injection pump typically dislikes to be run dry and will sometimes not prime when the chlorine tank is refilled. There should be a priming knob/valve atop the pump. When turned 90 degrees to detent, the air in the line is forced out. You should have a discharge/priming hose that returns to the chlorine tank and can watch the pulses from the pump when the priming is complete.
It's a high maintenance system if something goes awry, but when it's running well, it's great to have clean iron-free water. If you discover that it's the injection valve, buy a quantity and replace them on a calendar basis, rather than on a failure basis. I get three months between changes and have no more injection lapses.
Other types of systems can be found at the clean water store web site which effectively changes the method that triggers/measures/dispenses the chlorine. The above description is one of those at the site. The image below comes from this site.