A single zig zag is a bit problematic on single fabric thicknesses unless they are pretty stiff.
As you found, on its own, triple zig zag works better simply becuase the gap between successive stitches is much smaller, so there is less to "pull"..
A proper overcasting foot makes a big difference as it holds the thread over the edge of the fabric while the stitch is formed.
If you are brave enough to do it, dropping the bobbin tension as well as the top tension is likely to help a lot.
If you have a machine with a separate shuttle that holds the bobbin (Berninas for example) some folk have a second shuttle that they adjust according to what they need to do and use that if needed, leaving the original one untouched.
For some reason, bobbin tension adjustment is now feared and often recommended against by those who don't understand it, but there is no magic about it. If you understand what you're doing it can solve several problems.
The older machines told you in the instructions how to adjust it, recognizing that there is no one size fits all for it.
Unfortunately, if you have a modern horizontal hook machine, it is not really practical to keep changing bobbin tension and then returning it to "normal" every time.