It appears that once an input control is attached to a report in the JasperReports server view of the Jaspersoft Studio, you cannot re-order the input controls.
Input control order is very significant to end users. As reports evolve in response to end-user requests, additional input controls are often added and the order of them is often not correct (newly added input controls are listed "at the end" and sometimes need to be higher up to make sense to where the end user expects them to be).
The only way we can see to do this via Jaspersoft Studio is to delete all the existing input controls that come after the position where a new control needs to be added, then add the new control and then re-add the controls that come after. For pre-defined controls that are merely linked to the report, this is a pain. For custom controls, which involve embedded queries and formatting, it's incredibly error prone, tedious, and time-consuming.