Crape myrtles can be divided as you describe. To minimize the likelihood of failure, I'd wait until dormancy, remove all the soil (bare-root your tree), and carefully consider where to divide. With the soil gone, you will be able to minimize the amount of root damage and hopefully divide the plant more equally.

You may also use a shovel to chop around the roots of the tree and new ones will comp up. You can then dig them and have a new plant.

I would not mess with the root system this time of year.
I took 600 cuttings from Crepe Myrtle and stuck them in a misting bed on 9/2/09 and I check them this morning and most have roots on 9/21/09.
I will overwinter them in the rooting trays and pot them up in the middle of March 2010