Thanks for the info. First, if you can, a little heater will really help Judas. Bettas are tropical fish and need warm waters around 78-80 degrees farenheit to thrive. If the water is too cold, they become sluggish and lay around a lot.
Secondly, how many pellets to do you feed at a time? The best way to feed a betta is to offer several small meals throughout the day (breakfast, lunch and dinner!). Offer 1-2 pellets each time, no more than 6 maximum. And I just want to warn you that too many pellets can cause constipation, which can lead to some serious problems. One way to avoid this is to offer fewer pellets and substitute frozen or freeze-dried bloodworms or brine shrimp. Just a teeny bit, no more than half a worm or a tiny crumble of brine shrimp. A betta's stomach is about the size of his eye. Super tiny.
Do you know how many gallons your fish bowl is? If it's only a gallon or two, then you'll want to change the water at least every other day, preferably more. You can change 100% every other day or, if possible, change at least 50-75% every day. The more fresh water your guy has, the healthier he'll be. Is water softener the same as water conditioner that removes chlorine? I use API Stress Coat but there's also Seachem Prime and Tetra AquaSafe, as well as a few others.
If you can, I'd really advise you get an ammonia test kit. You can get strips that are less expensive but might not be as reliable or you can get a liquid drop kit. If you can test the water for ammonia at least once a week, this will help you to know if the level gets too high. If there's too much ammonia, Judas can suffer from ammonia burns and get infections or get ammonia poisoning
It sounds like Judas probably has ammonia poisoning and the best way to fix that is to do a 100% water change every day for a week at least. Also keep adding the aquarium salt for a few more days. It's 1 tsp per gallon. The aquarium salt will stimulate his slime coat, which helps him stay healthy and fight off diseases.
For now, don't worry about getting him to eat. You can keep trying but if he doesn't eat his pellets within ten minutes, remove them so they don't dirty up the water. I think he'll get his appetite back when he gets into clean water. It might take a few days, though.
I really hope Judas recovers quickly for you. I can't promise anything 'cause it does sound like a more serious case of ammonia poisoning but I really hope he gets better. Keep up with the water changes and if you can, get him a heater.
Hang in there.