Will this create $20 a month of value for them? If yes, charge $20 a month, pay e.g. Twilio $2 a month for your most active users and mouse droppings a month for the majority of your users. Problem solved. If your app does not create $20 of value when getting someone's attention 200 times, why bother making it?
There's a app out there which, essentially, provided a particular type of SMS services to a user population who thought SMSes were expensive. They grew like absolute wildfire, because the company underwrote their SMSing. They had no monetization in sight, because their core customers were too poor to pay for SMSes, and (luckily) got acquired before their telecom bill exceeded several million dollars in funding. If that is a trajectory which sounds appealing to you, well, that's an option, too.