Hi, Tim...There are two photos here, each looks like an original, worn brass ring. The one at the right shows the plates/keys cutting away at the brass. The damaged ring was rotating considerably. What was the condition of the plates/keys at the 3rd/4th gear synchronizer?
The ring at the right has straight "arrow" shaped teeth; the ring at left has offset/angled teeth. The ring at the right should be 4th gear for your later, 1999 AX15 unit. Correct?
Since I cannot see the new ring (please upload the third photo), I'm not able to determine whether the new bronze ring has straight arrow shaped teeth or offset teeth. As Gary suggests, on these later AX15 units, 3rd gear has a unique cog tooth arrangement (angled ramp shape, not arrow shaped). This fits with a unique brass ring design (which has offset crowns on the teeth).
The generic aftermarket rebuild kits apparently do not have offset teeth at the 3rd gear bronze synchro ring. Aftermarket kits often pattern a specific year(s) design. The earlier AX15 has arrow-shaped 3rd gear cog teeth and arrow-shaped teeth on the bronze ring—not the offset or ramping design. Both my magazine rebuild article and the Weber State University video demonstrate an earlier version of the AX15: 1990-92 vintage.
This 3rd gear synchro issue came up in JayDLogan's AX15 build, which is also a later Wrangler application. He and GaryT discovered that Chrysler/Mopar offers a unique part number for the 3rd gear bronze synchro ring plus a unique 3rd speed gear for these later AX15 applications. (I can furnish Mopar part numbers for the '99 3rd speed gear and the 3rd gear bronze synchro ring if you need these numbers, Tim.) In this topic's threads, GaryT uploaded photos of the later 3rd gear design found in his '99 TJ Wrangler AX15 rebuild.
GaryT, Jason (JayD) Logan and I have each raised questions about the bronze ring for a later AX15 3rd speed gear. The angled/ramping gear cog teeth may require the offset-point bronze ring teeth like in your photo at left (presumed to be the 3rd gear bronze ring?). Please clarify which ring fit where in your AX15, Tim. 4th gear appears to be the badly damaged ring at right with straight-arrow shaped teeth.
Aftermarket suppliers may need to offer an "early" and "late" rebuild kit—or specific "early" and "later" 3rd gear bronze synchro rings to accommodate the 3rd gear cog/teeth design change.
For some solid insight here, I started a brand new thread (click here) on the 3rd/4th synchronizer design change. Jason Logan (our fellow forum member JayDLogan) and I began an exchange just before these forums launched...I revisited that Q&A and added our exchange as a new thread.
At the new thread, you will find some insightful photos by Jason plus a valuable clue: the later AX15 transmission uses a different 3rd/4th gear synchronizer shift sleeve. If installed backward, especially with the wrong synchronizer ring match, this sleeve would raise all kinds of trouble with shifts between gears!
Take time to read and review the photos at the new thread, Tim. Our discussion should resonate...