You have two other solutions. You could build the app with an entreprise itunes account ($500/year) and people would just have to download it from a webpage (no app store required). You would have to protect this page though, so that only patient can download it.

The other solution is more a hack. You could use apple beta program (testflight on itunes connect). With this, you can distribute the app up to 1000 people, you just need their email. It's a little more complicated, and it's more a hack than a real solution.

I would love to help you out a bit further, https://clarity.fm/matthieurouif
and schedule a call if you want.