Hi Nick,
Correct me if I am wrong, but I think your Wood ancestors are not in your direct male line, as they are connected to your paternal grandmother, so a Y-DNA test would not be appropriate to find a Wood connection. Y-DNA is only for finding your male line, as the Y-chromosome is passed down from father to son ad infinitum. This is why my brother had to provide the sample for our test. You would also not have inherited your X-chromosome from your paternal grandmother, as this is passed down from your mother (and mother's mother etc). There is the new autosomal test which can determine cousin relationships back five or six generations and this is for both sexes - I am not sure under what circumstances I would use this as I have not looked into it closely; it may be something to look at if you had groups of people of the same surname with similar DNA.
You might like to try the Y-DNA test to find your haplogroup, which in turn would give you some idea where your male line originated (if as you say it is unusual and possibly French). This could also give you information on your deep ancestry - for instance if you wanted to participate in the Genographic Project. Other than that, if you have a good paper trail, and you're not interested in the French connection, why bother?
And yes, you are right; 7x g-grandfather may have had seven sons and we could be descended from any one of them - unless we came up with an exact match (0 genetic distance match) it would be hard to pinpoint. Of course, the more people test, the more likely it is that we will get a closer match - we will be patient and see what happens.
Tisy