If you want instead to remain with Google, you can distribute the app with your API Key and limit the usage to remain inside the free monthly quota.
What I have stated is that as you open the app and load the map, Google counts one call to the map API. Then you can zoom, pan as you want with no additional counts.
Play with the console to verify this.
I dont' how many user are you pointing to, but if you limit the usage for example to 50 calls per day, you can have 50 user that open the app per day. Maybe it is enough.
The only little unpleasant aspect is that you must anyway create an account and give Google your billing information with credit card also.
But as you stay below the free quota you will receive invoice from Google with 0 to pay.
For my purpose I have allready a google account and I gave also billing information and credit card. But this isn´t the intention. The planned tool I like to be free, because
GIS could be very helpful to solve problems. There exist for example Quantum GIS as opensource, but this is to fat for beginners.
The number of users I can´t estimate and there is the great risk. I know only that it is a worldwide problem and I don´t know how many people will use it.
Therefore I´m looking for an alternative.
I tested also the Google counts on the map API, I can´t confirm what you say, but maybe I made a mistake. From loading to zoom in I had 3 counts.
However I didn´t like it and I need another way. For myself I can controll my activities.