Mobile App Expert. 60 million downloads on last app.
Awarded "Best app of 2015" by Apple, "Best app of 2016" by Google
Expertise: Apple iOS Development & App Store Listing & ASO.
I have launched over 40 iPhone mobile apps (4 apps ranked #1 around the world). I am currently working on Replay which won the Apple "App of the year" award in 2014. I started doing apps 10 years ago while doing a master at Stanford. I've tried a lot of things and saw what work. I've become very effective at using app store search optimization strategies and gave multiple talks about it in front of hundred of developers.
I also have worked a lot with mobile technologies and iOS development developing the apps myself : GPS, iBeacon, Push Notifications.
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.