LED Strip Power Supply needs to be unplugged/replugged to work
OK here's the problem.  An amplifier does not actually combine power supplies.  It simply uses the 5 input channels only as a signal to switch the power supplied to its input.  All the strips downstream of an amplifier are powered only by the supply to the amplifier!   

So what you've done is hung all the LEDs on the #2 power supply, which is only sized for a single 16' (5m) strip.

The other power supply drives nothing but the controller and amplifier's internal loads, which are very small.  That might be a problem too. 

Option 1, leave it like this, and make sure power supply #2 is sized to drive all LEDs. I don't get why to have supply #1 at that point, just split power off supply #2 and do it all with one. 

Option 2:

Move the splitter so it takes the output of the controller and splits it to strip 1 and the amplifier.   Thus, power supply 1 will supply the controller and strip 1.    Power supply 2 will supply only the amplifier and strip 2.