How to fix error in actor component vector animation loop?

Could you elaborate on “effectively
integrating across the curve”?

I am referring to performing integration from calculus. Basically your blueprint calculates the total area between the curve and the 0 line. Since there is a greater area below the 0 line than above, there is a net movement in that direction.

More to the point, is there anything
in the repertoire to sort of force the
ticks to exactly follow the curve?

You don’t want to force ticks to happen at a certain time, instead you want to make the pipe be where it should be whenever the tick happens.

Is there a way to tell it to go over
the curve one step at a time rather
than accumulating (random?) relative
adjustments?

Yes, see my attached example.

By static multiplier do you mean like
a base vector to be added/subtracted
from the vector curve output?

Yes, it could be a vector position that your timeline output is an offset from, or a vector/scalar that your output vector is scaled by, or both. See my example for an example of a scalar value that the output is scaled by.

Do you know of anything you could
point me to that shows timers and
timelines working together?

I am attaching a picture of an example that I put together quickly. Since your timeline loops forever, I don’t believe you need to call it on every tick.