For me, my first time was in February, and I had a friend of mine teaching me. Except it was a similar situation to you, he didn't explain things too well, which can happen with people who have been doing something for years as they just automatically do things without consciously thinking about them.
So I wasn't making much progress til he said get off the green runs and go on some blues, you need more speed and more room to really get the hang of things.
And it worked. Beautifully. But, I learn by doing, not by theory, watching, or listening. I can grasp the basic idea of things through those, but until I fall on my butt about 10 times, I don't really know it.
So, my advice for you before you shell out cash for private lessons, would be to watch some videos first. Get the idea of what you need to do. Then go to some blues and just do it.
There is no substitute for practice.
So long as you have that heel edge, which you do, you can slow yourself down, stop, go at your own pace. Whereas unless you have an awesome smaller ski resort, it is doubtful the instructor is going to go out and board with you, much less for more than an hour or so.
Anyway, my two cents