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By transposing the data, moving rows required to move via the Multi-Row Formula Tool, and then crosstabbing the data back into its original form we are able to move the columns in a dynamic way.
The tricky part is in making sure that all columns downstream of the column requiring moving are flagged via a multi-row formula. Once the data is grouped into "Keep these values" (Flag = 0) and "Update these values" (Flag = -1) it becomes easier to approach the problem.