Problem is, it seems that maybe you think you are the only one trying to help someone. I'm also trying to help the OP.
Anyone wondering about this issue needs to look at the picture above. Ignore the end of my fat ugly finger but look where it is pointing. This is a Burris insert. A Burris Signature insert. A Burris Signature Z insert. NOT an XTR insert. The picture isn't the best quality but I believe everyone can see that where that ugly fat finger is pointing, that outer surface of that insert is ROUNDED. It is ROUNDED around it's radius and across it's width. The INNER body of the Signature Z ring is also ROUNDED. Bottom base and top strap are both ROUNDED internally around the radius and across the width, to match the ROUNDED shape of the insert's outer surface. Those 2 ROUNDED surfaces fit together. Much like a Heim joint, for the car guys. That ROUNDED surface matchup allows the insert to PIVOT front to rear as different height inserts are used so that the insert "self-aligns" within the ring body while staying in flat contact with the scope tube. This keeps the flat inner surface of the insert (where it touches the scope body) from contacting on an edge anywhere.
Then look above at any of the pictures above of the XTR inserts. The XTR insert is FLAT on it's outer surface. The inner surface of the XTR ring isn't rounded, it uses a raised central "ridge". THEY ARE NOT "THE SAME". Both Z and XTR use polymer inserts to customize "tilt" angle of the scope. Both types allow different thicknesses of insert to be paired to change the "tilt" (angle) of the scope. Both allow different combinations of inserts between front and rear rings to provide even more customization of "tilt". Both can be rotated around the inside diameter of the ring to change the orientation a bit so that some windage correction can be gained, although some elevation change is sacrificed to do so. But the SHAPE of the two inserts is PHYSICALLY DIFFERENT between Z and XTR and the inner shape of each respective ring type is different as well. Look at the XTR pictures above. The XTR appears to use a central elevated rounded "ridge" in the ring base and top strap (visible in the above photos) to allow PIVOT between that ridge and the flat outer surface of the XTR insert. The Z system, in contrast, uses a rounded inner ring base and top strap working with a rounded outer shape of the insert. Z inserts are intended to be used with Z rings while XTR inserts are intended to be used with XTR rings. They sure don't appear to be designed to be interchangeable. Would one type "fit" in the other? Possibly. But I absolutely do not believe that was intended by Burris and I don't believe such a possible combination would be as stable as would using them together as apparently designed. They are distinct designs, distinct shapes.
Considering the flat surface to RIDGE contact design of the XTR, I assume that would provide PIVOT front to rear. That appears to be how Burris designed in the PIVOT for the XTR-using the raised ridge to provide a PIVOT area. Two distinct ring designs, not intended to share inserts.
If one considers the contact area of the more spherical shape of the Z INSERT TO RING contact area (rounded to rounded) to that of the XTR INSERT TO RING contact area (raised ring ridge to flat outer insert surface), it sure seems that more contact area would be present with the Z rings than the XTR where the insert touches the ring. That COULD be more stable, more consistent because of more contact area. Maybe there is no functional difference for shooting. Maybe the XTR rings have ENOUGH contact area to work perfectly well. I don't know, I don't have any XTR rings at this time. But I don't base my information just on "what I've read on the internet". I did order a set of the XTR rings when they first came out. The height of the rings wasn't what I needed and I returned them. I did, however, look at the XTR rings out of the package and I did not like the contact design between the ridge on the ring (very narrow) and the flat surface of the insert. The functional design of the two ring types is a bit different and I returned the XTR rings to Midway and they exchanged them for Z rings. Is one better that the other? I don't know. I already had a few sets of Z rings in service and had seen no movement of any type so I elected to continue using the Z rings. It seems that the Z rings COULD HAVE much higher contact area between insert and ring-rounded/rounded contact vs narrow ridge/flat surface contact. But it also does appear that the XTR rings are usually wider (front to rear) and I believe they often have more screws attaching top strap to base so they possibly have more contact between insert and scope tube than the Z rings may have. Which is more important, if either? I don't know. My Z rings are very stable. I assume XTR rings are also very stable for those who use them. I didn't try the design after looking at it.
Assuming that the contact areas for the XTR rings (the flat outer surface of the insert contacting the raised ridge on the ring body) is designed to allow the desired PIVOT, then the inserts MAY POSSIBLY NOT be directional. I still don't know for certain but that is possible. I said from the beginning that I wasn't certain either way but that I believed that they were directional because of the offset number position. I still wonder WHY Burris moved the numbers from center of Z insert to side of XTR insert. But looking at the design it follows logically that they may have been moving the stamped number AWAY from the central area of the flat insert surface where that would be contacting the raised ridge of the ring to prevent the raised ridge from possibly flattening the numbers or making them unreadable. I don't know but this does seem to be logical.
Conclusion-maybe the inserts are not directional. I now think that maybe they aren't. But the two insert types are not "the same". They are different shapes designed to function in a specific way with the correct pairing of insert type to ring type. XTR with XTR, Z with Z. I prefer the contact areas provided by the Z design over that of the XTR design. I might be selling the XTR design short and they may be working perfectly well for people. I might have kept the XTR rings I ordered long ago had the ring height been usable. Maybe I'd have a different view of them in that case and maybe I'll try another set at some time. I've become a devoted user of Sportsmatch rings (on both air rifles and centerfire rifles) because they allow independent elevation and windage adjustment and they are perfectly stable once locked. I haven't purchase a set of Z rings in probably 5 years and may never purchase any more because I prefer the Sportsmatch.
No hard feelings. Just a disagreement. Isn't the first and won't be the last. Shoot well.