iPhone 5S apparently dead

First, not all screw holes are connected to ground. Use the SIM reader as that is easily accessible and connected to ground.

Second, seeing as how this follows a screen replacement, I would double check my work and insure there are no damaged flexes (screen) and that the connectors and surrounding area did not sustain any damage or debris. The iPhone 5S is prone to developing Long-Screw Damage (LSD). This occurs when the screws for the LCD retaining bracket are mixed up and a long screw goes where a short one should be. This damages the pcb and cuts traces that pass directly underneath the standoff.

I would also re-install the original screen to see if that makes a difference as low cost/quality screens can be problematic.

If the screen makes no difference, then you most likely damaged something on the logic board. Continue your probing and if the 0V persists on VCC_MAIN, then you have a short somewhere that needs to be found. Depending on your skill level, you could either hunt it down yourself using the schematic and boardview or have it looked at by a reputable shop that does micro-soldering work.