Turned bag - Wrinkels

Hi everyone I hope you're doing well!

I haven't been very active on here lately but looks like I'm back :) The latest bag I made was a bag which needed some reinforcement material and also had to be turned inside out in the process of it being made. I've made some turned bags before. You know, totes and such but never really had to put in some reinforcement in one. This was the first time.

For this bag I used 0.2 mm skin-flex as bag stiffener and everything was going fine until I turned the bag over . Even though I was very careful while turning it over the bag came out wrinkled.

I managed to get most of the bigger wrinkles out of by ironing the inside of the bag with an iron on the lowest heat setting. But its still not looking to good in my opinion. I made this video so you can see what I mean with wrinkles:

My question to you guys. Did you come across this problem yourself? And if you did, how did you solve it. Do you have any suggestions on how to avoid this in the future?