A one stop fix would be to get VPN as a service to quickly fix networks that block based on ports or deeper packet inspection.
Start with this free option to be sure VPN aren't blocked too.
The next easiest option would be to make configuration profiles to push to the devices. iOS allows easy push of mail configuration profiles to automate the tap, tap, tap, type chore of changing ports on multiple accounts. I recommend you start with a free hosted MDM that's also reputable.
There is some setup, but if you're already running Mail servers I would expect the setup to take about 30 minutes top to be running with your push certificates, one device enrolled, and push custom mail settings to that enrolled device.
Basically, you would:
- Sign up
- Follow the Push Notification
- Make a blueprint
- Define one mail server profile like I show above
- Enroll your device in the MDM
- Choose the bluerint that has your mail settings
- Profit for ever more now that you have an MDM to automate your iOS team devices.