Have you considered the YDNA test? We have had success, in some cases, in assigning people to a family that has much more ancestral information than the tester had. This is no certain remedy, as can be seen from the approximately one-third (about 50 of 150) of the Alexander DNA-testers who have not found anyone closely matching them. For me, it confirmed that family tales had some truth behind them, and, also, I've found a bunch of cousins. If you decide to test, you would be more likely to find matches with the FTDNA tests than others because that is what most of us have used; however, you may wish to wait until they offer a special discount for the test, which they and other companies do periodically.
The Alexander DNA page is currently in a bit of a mess because I am updating and revising it; however, if you get in contact with me, I'll send you the information on the families we have (and give you contact information for the project administrator, Roger Alexander).