Dave as usual hits the nail firmly on the head. I've got the Tracy Marks book and used to use it a lot. She does give a series of 'compensations' for lack of particular elements. I've also seen attempts to bring in compensation through allocating elements to the Houses (Fourth, Eighth and Twelfth as 'Water' Houses)
Marks also gives double weight to Sun and Moon and includes the MC and ASC in the calculation (which your initial count did not). So you may actually gain Water from the inclusion of the latter two.
I also think there are serious issues with this approach to 'elements' Firstl, the count includes the outer planets, which are assumed to be generational not personal. They certainly should not be weighted as much as the others (if at all)
Secondly, it's too simplistic. It assumes that the planets themselves have no influence on the outcome, only the signs - and that is just not the case. The planets bring with them Heat, Cold, Dryness and Moisture (Fire is hot and dry; Earth is cold and dry; Air is Hot and Moist and Water is cold and moist) - so you might find they gain moisture through certain planetary placements.
The modern approach makes no allowance for the seasons or for the Moon's phase, for example the traditional view is to take the Sun according to the season of the year - so if one or more of your nieces is born in Spring or Winter they will gain moisture.
I could go further but my point is really that you need to take care with a simplistic approach there are a lot more things that determine a person's element balance than the sign placements of the planets.
If you are using a modern approach I'd suggest you have a look at Stephen Arroyo's 'Astrology, Psychology and the Four Elements', which will give you a more detailed treatment. I agree with Dave that you can't get everything out of books, but you do have to start somewhere.
