Deploy iOS app on personal devices
If you're willing to pay the 99$ yearly Apple Developer Program enrollment fee, the easiest option for you would be to use "Ad-hoc Distribution". This is slighly more involved than TestFlight, but will allow your users to use the app for a full year instead of 90 days.

Essentially you need to get the UDID (unique ID number visible in iTunes or on the device) for each of the devices that you want to deploy to. You add those UDIDs to in the Developer Portal and then you sign the app with your certificate and add your provisioning profile with the UDIDs in (these steps are automatically done by Xcode). It is really much simpler than it sounds like.

You can then install the app on all the devices for which you had UDIDs. They will last a year before you need to renew your enrollment in the developer program.

Note that you do not need the Apple-IDs used on the devices you want to deploy on (in contrary to TestFlight). Therefore you will not have the same problems with Apple-IDs here.

Another option is to use the more expensive (299$) Enterprise Program (note that you need to own or otherwise be entitled to sign for a business to enroll). Here the signing certificate is valid for 3 years, however the actual provisioning profile still expires after 1 year. So you would need to pay the fee every year, and users will need to be online to renew the profile, etc.