You might find the Abbott Freestyle Libre worth trying. It tracks your blood glucose, but updates intermittently rather than continually like a CGM. Whenever you hold the reader close to the sensor it updates the blood glucose graph so you can see what's been happening, and the trend.
The reader and 2 x 14-day sensor pack are reasonably-priced, around £160 so if you don't continue there isn't much downside. However it's only available in the UK, France, Germany, Italy, the Netherlands, Spain, and Sweden. They wont ship outside those countries so you'd need a forwarding address. US maybe March 2016. And there's a waiting list as they can't keep up with demand.
However it will give you a lot more insight into what is going on overnight. It's particularly helpful in setting basal doses.
You may find that two basal doses per day help, allowing you to reduce the overnight dose relative to the daytime dose - that fixed my overnight hypos.
Of course a pump can do that too.
But first get the facts before you jump to a conclusion.