My Thoughts
I dont know much about ACRA or any related library for this purpose. But if i had to implement this.
At the time of crash happening. From UncaughtExceptionHandler custom implementation. I would save logs to a file instead of sending that right away to server.
Wait for next app start and send it then to server.
Using whatever to you want service, async task , loader. I would have gone for service to do this in background spawning its own thread.
Now logic and algorithm can be applied to send only mined data or mining can be done at server end. Upto the designs