I used to run with stability shoes (Nike Lunarglide 1-4) and I had plantar fasciitis off and on for 4 years, finally resulting in a bone spur in my left heel that was caused by a severe plantar fasciitis. Eight months later and thousands of dollars spent on physical therapy and podiatrist I was finally cured. Fast forward to now two years later I am completely healthy and the plantar fasciitis never came back and the bone spur is still in my heel, but I can run for however long I want without the plantar being aggravated.
Here's what worked for me and in the same order:
1) Go to a physical therapist that actually runs and understands running.
2) Strengthen your IT bands, hamstrings, arches, and calves (working with a resistance band or TheraBand).
3) Don't run in shoes that have any built in arch support and focus on shoes that have anywhere from 0 to 8MM drop from the heel to the forefoot.
4)Go to amazon and look up the powerstep pinnacle insert and get one of those instead of shoes that have the built in support. They are like 30 bucks and you can wear them for like a month and then try to do a shorter run without them and you should be fine.
All of the above worked for me and I've tried every little thing that you can to relieve plantar fasciitis. The arch support in shoes hurt my arches in the same way that it did to yours.
I hope I've helped and good luck with the injury.