It sounds as your basal needs adjusting...
Have you considered doing a fasting basal test to indentify where the problem lies, as it sounds as if your basal is out.
I know a lot of clinics aren't keen on basal fasting tests but it's the only way to find out if the a problem lies with the basal or not!
As long as you do it wisely, on a day when you aren't doing extensive exercise, so do it on a rest day ensure that you've got a good supply of test strips and hypo treatment... Do your testing and be prepaored to abort the fasting test if your BG goes too high or you become hypo...
I tend to do a fasting basal test of one of my sectors (24 hours split into 3 sectors) once a month, unless I've got a problem that I want to sort.. As you do find that over time your basal needs to change slightly and need adjusting, by testing a sector every month it means a tweak rather a major asjustment to sort out problems