This is a REALLY odd solution.
RMB on the dimension then Properties.
Now on the Lines and Co-ordinate tab set the Break Line Gap to a NEGATIVE number.
So if normally it's 1.5 set it to -1.5
There is quite a simple method of moving the dimension value and that is to first click and hold the number with LMB, then press and hold the shift key. You will then be able to move the location of the dimension value.