Draw a line at the desired joint position through the critter, duplicate the critter and line, then with the shift key down move the critters to opposite sides of the wrap, aligning the line(s) at the edges. Delete the lines, group the critters (in case you want to move them).
NOTES: The box around the rope must extend beyond the edges in order for the rope to be continuous. Rope alignment was achieved by using a line across the rope at matching points then stretched a bit to get the lines at the wrapped part edge.
The individual dishes were created by using the create vector boundary then an offset outwards.
The box and the dish on the bottom stick extends beyond the edges just like the rope does, otherwise there will be a raised dish edge at the wrap joint.
There is another box around the carved area too. This box is used to define the actual carving area. (Hope this all makes sense, if not send me a note with your question(s))
Critters are 0.18" deep
Turned stick diameter 1.4"
Raster cut with a 1/16" ball nose bit using an 8% step-over
Dale