2P2222 Transistor Switching

CrossRoads:
Where is 650mA coming from?
Datasheet provided clearly shows Absolute Max as 600mA.

Memory. I can't be bothered to read PNG images that are 10x bigger than the screen.

There's some variation between manufacturers, eg. the Fairchild PN2222A has 1A max (!), see: Intelligent Power and Sensing Technologies | onsemi

You're right. The gain drops with current so you need a bit more current into the base.