Jake:
I see that your tool is trying to automate the Add Field, Calculate Field, Delete Field, Alter Field (to rename it) workaround steps that normally have been done when the original feature class/table is changed rather than creating a new fc/table. The Alter Field step of the tool will only work if the input is within a geodatabase. For shapefiles you have to do a second Add Field, Calculate Field, Delete Field to get the original field name back. Your tool should test the input to determine if the Alter Field step can be done and otherwise do the 3 alternative steps. Of course, this workaround technically is not altering the original field, just the original fc/table.
The unfortunate consequence of this workaround is that the fields are reordered, with the new version of the field being added to the end of the fc/table's field set rather than remaining in its original position, but if retaining the ObjectIDs of the original features/rows is important, your approach would be necessary. The only way to keep the field order is to create a new fc using a tool like the Feature Class to Feature Class tool as Gabriel suggested, but then all ObjectIDs will be renumbered (and I think that GlobalIDs also regenerate or cease to function).