Correct way to do "power injection" from multiple DC supplies?
Yep, you have it correct and the schematic you drew should work great.  Power supplies are, in general, NOT designed to be paralleled unless they are specifically designed for current sharing. Read the data sheet for the power supply. If it does not call out current sharing, then it cannot be used in a paralleling scheme. 

Of course the grounds must all be connected together so the signaling works correctly but HOW you do this can be important. Each PSU GND should be connected to the load (LEDs) just like the VCC connection with the appropriate wire gauge.  In addition a global GND wire should connect all of the GNDs together preferably at the LED module GND connection. The idea is that the GND voltage at the LED modules should be at the same potential as the controller GND for the best communication robustness.