I don't really have a great answer myself, personally. That's partly why I made my post to begin with.
However, one thing that I think would greatly help is a privacy notice of some sort detailing exactly what is tracked and how it's used. I don't see one on either the Play store page, nor in the app itself (your site seems to be loading slowly at the moment, or I'd look there too). While it may not completely remove my fears, it would at least serve as a good baseline and would make me feel a little better.
EDIT: Tried your site again, and found your privacy policy. I must say, I do like the way it is written as well as the content. Still, I would encourage maybe a link in the app, at least.
The topic of trust deserves a lot of attention, thanks for rallying some attention to it!
An idea: trust is a huge issue when it comes to development of apps (mobile or otherwise) that transacts important data (and what doesn't these days? Even games could be used to create personal metrics on people's IQ/skills/etc.). Some sort of consortium should be formed to work a coherent strategy on this, anything would pretty much be better than the current day situation: a combination of oath/register/proven-track-record-of-company/technical-guide-lines/technical-validation could prove very valuable resource to consumers and businesses alike!
However, one thing that I think would greatly help is a privacy notice of some sort detailing exactly what is tracked and how it's used. I don't see one on either the Play store page, nor in the app itself (your site seems to be loading slowly at the moment, or I'd look there too). While it may not completely remove my fears, it would at least serve as a good baseline and would make me feel a little better.
EDIT: Tried your site again, and found your privacy policy. I must say, I do like the way it is written as well as the content. Still, I would encourage maybe a link in the app, at least.