Thanks very much for the advice. The programmer is a little expensive for me to bother with at the moment given all the cost of all the parts I've already had to buy for this project, so I will just try and work it as it is for the moment and see how I go.
I wonder if an RC shop here in New Zealand would have such a programmer that they could help me tweak the servo with, just a bit...
I've accepted the fact that off is in the middle, and very sensitive. The only thing that's not great is how small a turn is needed to get the servo on its slowest rotation (a hair's width of a turn, if that).
Thanks again everyone. It's nice to be able to draw on such advice when I have no clue about these things myself. The thought of having to send the driver back to the States was a little stressful!