Generally - if the IRS provides a list of examples and do not specifically mention that the list is not limited - it is understood a complete and final list. The same would be the answer from most accountants or tax persons and - that is more important - from the IRS agent in case of audit.
However - in this specific situation the IRS mentioned that officers of charitable organization are deemed to be employees by statute. - http://www.irs.gov/charities/article/0,,id=131138,00.html
I would just use this fact to proof that the IRS doesn't limit the list by four categories that they provided.
In California - in the motion picture, radio, or television industry, an artist or author may be treated as a statutory employee under certain circumstances -
The document also mentioned that statutory employees may be in construction industry.
That are additional examples outside "the list of four" provided by the IRS.
A statutory employee is defined as an employee by law under a specific statute. In Virginia - that may be Workers' Compensation Act, that requires to treat certain workers (like you) as employees - anyone employing three or more people must secure their liability either by insurance or other means acceptable under the Act - http://www.vwc.state.va.us/employers_guide.htm
While I do not see any direct source that may be used to support the employment status in your situation - as you are not clear fall into any of these four categories - we are in a gray area - I do not see any limitation based on your information that would prohibit such treatment. However you may do such determination on your own - the determination if you are indeed a statutory employee (and the responsibility for such determination) - should be done by your employer.
If your employer decide that you may not be classifies as a statutory employee - there is nothing you may do to force such decision.