Short version:
In my tests with Android 5.0 Lollipop I have noticed android.bluetooth.le.BluetoothLeScanner detects BLE devices less frequently than Android 4.4 KitK
I have experienced very similar results with my Nexus 4, in both KitKat and Lollipop.
With KitKat the bluetooth adapter also eventually went unresponsive; at first I though that it could be related to a short scan interval (200ms) but increasing that number to even a second didn't help, in that matter I found that, when unresponsive disabling and enabling the adapter programmatically, sometimes solves the problem. Unfortunately I can't say that it works all the time.
Now with Lollipop, in which I had high hopes to solve this issues, I experienced the same behaviour that you describe. I also had to use the startScan / stopScan implementation, getting similar results regarding the detection times. Sadly, I haven't found a work around to get results more quickly.
Based on what you describe I suppose it could be a hardware issue, even though the Nexus 7 and Nexus 4 are from different manufacturers (Asus and LG).
I know I'm not providing much help here besides trying to answer your question about you missing something; I don't think so, I think the problem is something like the hardware or the bluetooth API that still doesn't behave the way it should across different devices.