sanUK,
If you put the lights directly under the tree, they will only light up the lowest of the branches.
I'd personally go with your own idea, but bear in mind that you are probably going to need narrow beam spot fittings.
How tall is the tree?, I used to live next to one of these trees and they get pretty big.
I don't think that the customer would want it lit right to the top, would they?.
One other thing, is to make sure that where you position your luminares, that they will not annoy any of the nieghbours, there is nothing like a bright light shining straight in your bedroom window, especially if it is not yours!.
Hope this is of some help.

Mike Trump.