Based on your desciption of the bracket, my money is on the cause being the loose screws you mentioned... But it is possible that the poping is at the rod ends as well if these are worn down. To check for this is really simple; lift the passanger side wheel up, and try to rock it from side to side. If there is any movement, then the rod ends are your problem (the reason for the passanger side is that ussually right hand turns are taken at higher speeds than left hand turns, so this side wears out faster).
By the way, just as a general comment, I have this popping myself, so I was doing some research on the subject. I have not yet checked out y track bar (it's on a different location on the YJ, but has pretty much the same effect, and tends to have this problem when trackbar relocation brackets are used), but I am still debating wether to remove the track bar completely or retighten it. I also need to check the rod ends for wear (the passanger side looks pretty much done for!) and most likely replace them.
Moz,
NICE IMAGE! What did you use? Photoshop? I should learn how to use that darn program!!!
Felipe