The only way to fix it is to consciously fix it. On top of those shoes, I would generally wear insoles in them for more stability and support. so I'm not sure that you have to wear stability shoes.
I say this because I hate stability shoes. And it's not just when I'm walking - when I'm standing naturally, my ankles sort of cave in toward each other. Or at least not have to wear stability shoes? But I feel like most people probably don't just "deal with" arch pain as a necessary evil of running. So yeah, is overpronation just a symptom of weak foot/leg muscles? I mean, if I do exercises to strengthen my foot/lower leg muscles , can I stop overpronating? I just took it as a trade off that I could either have painful arches while I was running or have sore arches/shin splints afterward.
Once you get used to it, it feels a lot better and I never have the sore arches problem anymore.
But honestly, anything is probably better than the 4 year old shoes I'm wearing now. And I don't mean by using stability shoes or whatever. I've also read a study that said more runners were injured wearing pronation controlling shoes than neutral shoes.