Is the hfe of a transistor dependent on the resistance on the other parts of the circuit?
There are two possible causes of the blown transistors. First, connecting the base directly to 3.7V will cause excessive base current : it makes sense to limit that with a resistor. 20mA is cautious, 100 ohms would allow 30ma which should be safe.

The second in that - while you cannot "push" excessive current like 2A to the motor - if it draws 600mA when running normally, it may draw much higher currents when starting, or when stalled. 

Connect the motor to the PSU again, and stall it with your fingers (don't do this with a high power motor! Use some other means of braking it!) Observe the current it draws when stalled ... I'm guessing somewhere over 3 Amps (you may need to fiddle with the current limit to observe this).

It will momentarily draw that current when starting, and that could be fatal to a 650mA rated transistor...