Did you reshape the lugs or case shape in any way? If so, the end links might need some adjustment to fit correctly.
The "tangs" (I'm not sure what the proper name is, so I'll go with yours, lol) are designed to put some tension between the part against the case and the bottom of the lug, but if you altered the lug profile, they'll need to be bent "up" a bit. They're in the picture in
RED
It's also possible the area in green might need to be opened up or modified slightly if a different size spring bar is used, or if the spring bar hold wasn't drilled exactly centered.
If it's any consolation, every single gen bracelet I have with folded end links develops play in this area. The trick is to bend the little tabs a small amount to properly "squeeze" the lugs, if that makes sense.