As a quick sanity check, have you tried comparing cable colours between each of the axes? There is always the possibility that a cable connector is mis-wired. The other standard check is to swap two axes - in your case, as far as I can see, you could temporarily swap the X and Z cables at the controller end. However, this is usually used to chase a genuine hardware fault, and it does assume that the configuration parameters for both axes are the same, especially the direction parameter here. The idea is to see if the error stays on the same axis or not to see if the problem is at the motor or controller end.

I really would try that "reverse axis" link - it takes minutes, cannot do any damage, and is just as easily reversible.

A lot of members of this forum have built or renovated their own machines - I've built two routers and updated or completely rebuilt the electronics in a CNC mill and lathe, and I'm a relative beginner here! - but that does give you an insight into how these things work, at the cost of a lot of blood, sweat and tears!

Here's another test you could do to prove whether something is actually broken, or just wrongly configured. Can you manually jog the Z axis via the control software without homing? If so, try jogging in both directions. If the axis moves both ways, you have proved that the hardware is all working, but there is minor wiring or software configuration fault. And that suggested "reverse axis" configuration change is a perfectly acceptable way of compensating for the wiring issue. I had this problem on at least two of the axes on my router when I first switched it on - it is that common a problem on a new machine. In an ideal world on a well-built kit machine it shouldn't happen but you may be able to fix it yourself quicker than waiting for the manufacturer. Then you can get to actually cutting things!