There are, in fact, a wide variety of techniques for producing graphene other than the scotch-tape method. A very good review of these techniques can be found in this recent review article:
It is extremely difficult to obtain the dimensions you require using the scotch-tape method. In my former group, even the student who was the best (in our group obviously) at using the scotch-tape method could go as far as 20-30 $\mu m$ long flakes. I am not aware of the world record for graphene flake sizes using this method. Our group, very soon, switched to the CVD method to produce large area graphene; we were successfully able to produce graphene on TEM grids using this method.
Since I don't know what your resources are, you may want to go through the above review article to find the method that is most convenient for you. My personal favorite is the layer-by-layer removal of graphene described in section 6.1 of the paper. I consider this method to be the chemical analogue of the scotch-tape method; except here you can precisely control the number of graphene layers!