Direct Inverse Filtering an image, spatially convolved with a blurring function without any noise, doees not give my original image back?
I think I found out the answer to my own question. 

Since I'm using an averaging filter mask (some constant multiplied by a matrix of ones), the Fourier Transform of such a filter is an impulse at zero frequency. 

When I pad the mask filter in step 1 to make the dimensions of the mask equal to the image, I am 'truncating' the filter, ie. windowing the mask, which is akin to multiplying the Fourier Transform of the mask with a sinc function. 

As a result, the Frequency Domain filter I use in step 5, ie. H, is not an impulse but a sinc function. That's the reason why my results are not ideal.

On the other hand, if I were to use an impulse in step 5, only the zero-frequency value would remain, and my result would be a constant image. 

In short, it's a lose-lose situation.