Broken zipper in tiered skirt

I have one of these fashionable tiered skirts but the zip broke (so
badly that my husband had to cut me out of it!) My question is, are
there better zips for this type of skirt, where the zip extends through
the horizontal tier seams? It seems that the effort of forcing the zip
through the bump of the seam is the problem.

Thanks,
Fey

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