Hi JK - great question. Doing some barefoot/minimal running will really help strengthen your feet and create a natural support/stabilization system in your feet. I too have very narrow and flat feet and thru the years I have strengthen them with barefoot drill and strength exercises to where now I have a normal arch and am not flat footed at all. DO NOT think you can train your flat foot - you can. Once you have made some progress your current stability/motion control shoes will become very painful in the arch - this is a good indication you are strong and could go minimal full time.
Try doing some barefoot one leg balance drills working up to 1-2 min on each foot. Then progress to balancing one foot on your forefoot only - very challenging and potent.
I noticed that this morning. I did 10min in my new VFFs. Started to feel a good ball of foot heel landing much lighter than usual. I gladly changed to my ghost gtxs, due to 28°F heavy fog with lots of puddles they are warmer. But immediately my heel arch hurt: I think the heels are too high. It took 5 mins to find a comfortable stride. I suffered from PF this summer and am still sensitive. I have to keep my cadence at 175+. Bruce