FFTW: Logical array size in r2r transform?
You're on the right track.  The distinction must be made between the physical size of your array, n (generally $n_0 × n_1 × n_2 × … × n_{d-1}$ except for in-place R2C transforms), and the logical size, N.  For a 10x10 matrix, the physical size is n=10*10=100, so the logical size for this particular transform is N=2n=200,  the scaling factor for the unnormalized transform-then-inverse result.

They talk a little more about that here in the Real even/odd FFTW3 docs, although they don't give much more info than the link you provided.

It's always a good idea to test with a problem that you already know the answer to,