Yep, I'm with Alan. There's an old rule of thumb that goes something like this: If it blooms in
spring (i.e.
lilacs), prune in early summer. If it blooms in summer (as crape myrtles do), prune in early
spring.
It shouldn't matter whether you prune top to bottom or vice versa, but don't take off more than a third of the total number of branches. In other words, if there are 24 branches, cut off only 8 this next
spring. You can do another third the following
spring, if you have to. Cut off each branch as close as you can to the main trunk, leaving just the little collar where the branch sprouts off from the main trunk. That will help the myrtle heal nicely.
The umbrella shape is nice. Very Japanese! Good luck.