I'm thinking that General Manager is below President or CEO but above Supervisor (which generally gives an impression of being lower down the ladder). He has a broad overall control over the company.
Here are some "統"compound word comparisons [source: Nelson's Japanese Character Dictionary]
統率する = command, lead
統率者 = commander, leader
統御する = control, administer
統領 = chief, manager, dictator
統監 = supervision; commander; resident-general
統轄 = control
統轄者 = the one in charge

With 統轄者 being "the one in charge", and with this position being known to be below president (and not V.P.) I would tend to go for "General Manager" or "Regional General Manager" as you say if he's the General Manager of a region. It's a position of high responsibility and control within a company.

Here are some website definitions:
http://management.about.com/od/policiesandprocedures/g/gm1.h...
Definition: A General Manager has broad, overall responsibility for a business or organization. Whereas a manager may be responsible for one functional area, the General Manager is responsible for all areas.
General Managers manage through subordinate manager. However, a General Manager may have individuals reporting to him/her who are not managers.
A General Manager has the power to hire, fire, or promote employees.
A General Manager is responsible for higher level planning than a manager. A General Manager is often responsible for the overall strategic planning and direction of the company or organization and leaves the day-to-day management of the various functions to the managers.
Also Known As: GM
Examples:
The General Manager provided strategic direction for the whole company.

http://wordnetweb.princeton.edu/perl/webwn?s=general manager
Noun • S: (n) general manager (the highest ranking manager)






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Note added at 5 hrs (2010-11-04 02:38:07 GMT)
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My pleasure, Jeremy. The GM's a pretty big deal! :-)