In my experience, slight stress best promotes flowers in Crepe myrtles. They are used to warm, arid climates (like Texas), and grow best in those regions. Up north, such as in New York, where you are, they won't bloom as easily, without certain conditions being met. Here's another instance of a northern gardener not being able to get their crepe myrtles to bloom. Here's what I'd try:
Stop irrigating. In their natural habitat, they often get along quite well naturalized, without trouble. Watering makes the plant grow more lushly, at the expense of flowers, similar to fertilizer.
Only fertilize with potassium and phosphorus, not nitrogen. Something like 0-10-5 or similar. This promotes flowering. Nitrogen promotes greenery, but not flowering.
The soil sounds good, even if it's low in nutrients. Crepe myrtles do well in poor soils. The healthiest ones I've ever seen here in Pennsylvania were growing in a dry sandy soil so dry and poor the weeds weren't even growing well.
Don't prune much; it encourages vegetative growth, often at the expense of flowers in northern climates.
For what it's worth, I transplanted a similarly sized one this spring, after it almost died over winter (I was replacing it with a dogwood for a customer, and thought it was worth salvaging) and it flowered right away. But it didn't grow much (maybe up to 6") before flowering. It is now on a very dry slope, similar to where it was before, and is recovering well. I expect full recovery within 3-4 years.