For something that will see water more frequently I would switch to TB2, the working time is pretty short, but it's a waterproof glue. I was looking at TB3 in the store the other day and think I might try it sometime in the future for segmented stuff.
As for your current problem, take a piece of paper, apply a lot of glue down a length of a few inches, then open the ring and do your best to slide the paper through the joint until it deposits as much glue as possible within the joint. Good luck.
I want to die quietly in my sleep like my grandfather, not screaming in terror like the passengers of his car.