Hey Brian,
"""""""""Create a centerline curve for each object.
Use FLOW. Select squiggly pipe as object to flow.
Select its centerline, then the targets centerline."""""""""""""""

Because of the disparate shape of the target, creating a centerline of the object shape will produce a result that folds over itself (I only made a centerline target from the XY plane and not the ZY plane to test)

So in that case, it should be a flow of just a single edge, which will allow the original shape to maintain itself. But it will just have to deviate from the target objects structure..