The Hat PCB is functioning as designed. Here's a photo of it attached to my Raspberry Pi 2 B.

I ran two discharge tests on this UPS version. The first was with the red Efest 700mAh battery: it lasted 1 hour 15 minutes. The UPS lasted 1 hour 51 minutes using the black KeepPower 800mAh battery. The load for both tests was an idling Raspberry Pi 2B.

The SOT23-5 battery charger gets quite hot when charging the battery with full current, but it doesn't appear to cause any problems since the charger has a thermal limit.

At this point I'm pretty much done with this project. I will let PaulV perform the 2-3A torture testing.

Here's a photo showing all three PCBs for comparison purposes.