If I common the TIU fixed 1 output to the Z1000 ground, the breaker on the Z1000 pops
If I ground the TIU fixed 1 input (Z4000 output gnd) to the Z1000 gnd, the Z4000 will read 1.4V when the handle is at minimum, and won't advance past about 16V at max handle (seems to load it down).
Also, at some point, the 20A input fuse for the TIU channel 1 blew (not sure when, because I was focusing on the switches, and not running a train.
You most likely have either an out-of-phase condition between your layout transformer sir some other wiring anomaly.
I was also using the 18v output of the Z1000 to provide aux power to the TIU - did I create some sort of a loop or conflict?
If you reversed the polarity for the Aux. power port vis-a-vis your track power from the Z4000, you generated a short circuit between the two outputs of the Z4000. I'd suggest using a different, separate, power supply for the Aux. Power port and see how many of your issues go away.
Is 3A enough to run the about 14 switches on the layout, realizing they don't all operate at once and only have momentary current flow?
That depends upon the switch tracks and whether they use bulbs or LEDs in the motors and the controllers.