We would like to know how the GcmNetworkManager actually schedules us over time (eg, how the intervals between service windows might decay). For example, batch 30 urls and be able to see how long it took to process full batch and also drill in to see when the service windows started. We could then run this on different devices (different OS versions and resources) to get some concrete knowledge and expectations. This may help motivate looking into augmenting the GcmNetworkManager scheduling with ConnectivityListener as well. 

I was talking with Yafei today and he may be pretty close to this currently. 
He might be able to provide two configurations - one that lets all processing go through GcmNetworkManager scheduling and one that calls StartProcessing directly to blast through a higher number of URLs faster.