I know some woman increase their iron levels on their menstrual period.
I don't notice a change but my bgs are relatively erratic on insulin so very difficult to pin point without my other factors (eg Stress).
I'm sure now you've been able to identify the cause something will be suggested.
Sorry I'm no more help.
They say type 2 is mainly diet controlled so I do suggest eating beef or other iron filled foods and see if any help.
I'll be interested to see what your gp suggests.