EDIT. I refer to your loop as a path but also a line/shape in Illustrator is called a path so I hope this doesn't confuse.
One way would be to draw over the loops with a single line/path using the pen tool.
I'd take as much time as needed to get the curves and the shape of it right at this stage.
Just draw through the middle of the loop and make sure it joins up again.
When you're happy with the shape, Just bump up the line width up to how you'd like it.
Select it then go to Object > Paths > Outline Stroke.
This will create a shape from the original line but you'll not be able to edit it in the same way as before.
You should notice that there will be an overlap where the paths cross.
With the image selected still, go to your Pathfinder window and select the "Divide" option and ungroup the selection.
You should now have it split into its separate parts.
It should look very similar to what you've drawn it this point without the rest of the tiles on the path.
Now your intersections should be just a single shape or tile.
You can leave them like this or, if you don't want a tile on the intersection, select that and the part of the loop that you'd imagine would
be on top, then "Unify" in Pathfinder.
To get all the individual tiles just draw lines crossing over it where you want them and with the whole thing selected go to your Pathfinder
window again and hit "Divide".
This should cut it all up into tiles.
Don't forget to ungroup them. When you use the "Divide" option it always groups them together.
That should 'hopefully' work but ask if you struggle.
