Invert/evert cylinder object (Inside out)

So far this is what I have, not using square wire though.

I point animated one loop section of the spline
then I used a Sweep Creator and Ring Modifier.

Unfortunately the Ring Modifier doesn't have a point snapping
option like the Symmetry Modifier does so gaps appear.

Trying to make square wire is a problem
as the Sweep Modifier rotates the profile.

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With some careful editing of the spline ends you can hide the gap.

I added one "spur" in the hope of using a Ring Modifier for the
rest but that didn't work for me so each spur would have
to be animated separately which is not hard to do.

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Here's a more finished version.

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