I think you are using a copy of the required toolpaths 6 times in your drawing if I am reading your message correctly? I think the easiest way to do this and not have any opened vectors is to edit the first complete set of vectors you draw and close all the vectors before you copy and paste it to the other locations.
When you select a vector or set of vectors that has been closed all of those vectors will be highlighted with a single click of the mouse. If you select a set of vectors that you think are closed and all of them do not get highlighted it is a clue that those vectors are not closed and you need to do some more work with them to find the problem area and fix it. Sometimes you will need to perhaps select the 2 vectors of the set you want closed and then right click and select the 'join vectors' command to connect the 2 selected vectors. You may have to do this several times to fix the opened vectors and then you will be able to use the 'close vectors' command to get the set of vectors closed.
This is not the typical way it works, but there are instances when vectors that appear to be closed and connected will be easy to see are not connected or closed if you zoom in close on what looks like the intersection points of the vectors. Many times I will find the lines do not actually touch and are not connected when zoomed in close, but from the regular view it all looks good. You can usually find the problem spot by zooming in on all the vectors. I hope something I have posted helps you, but if not or if you have other questions please ask them. I am also glad to try and fix the file if you can not figure it out, and you can send it to me at: email@example.com
I will be glad to try and fix it and attach an explanation of what was done if needed.