Yeah idk why, but when I found out I could do the jumping puzzles on the other maps, that's when I realized all other server maps have the same layout. I knew that seperate servers that played eachother had the same layout, but the whole time I thought that all 4 islands were unique. Its just eternal battlegrounds that is different and I just found out today. I feel kinda stupid cause I have been playing wvw for a while now hahaha.
In my experience these are not bound to the daily reset but to some timer of it's own - I'm not 100% certain that is the case but I've done the puzzles after daily reset and not had the chests available a number of times now.
How many badges does the EB puzzle drop? (20?) I find the other side BL's jp's to be worth it because they can be done in 3-4 minutes and I mostly do it for the siege, but the 6 badges or so per jp arent bad. The EB puzzle takes too long and is likely to have people camping it. Unless you want to run it in stealth, but the dark room is a pain.
You're better of spending the time you would have spent in that puzzle, with your main zerg (if there is one at the time) and pew pew from the back to tag as many people as you can...you'll get more badges that way in the same time.