Images from Photos to 16 bit Square/ Hexagonal Grid Images- How to create them

Hi Folks,
So I had an epiphany regarding a side project I am working on. Whilst the code isn't that bad the artwork is proving to be an absolute nightmare. Consider this, I have a photo and I want to have a scene where you basically recreated the image using grids which will have only one colour. In this case, lets say a 18R x 30C grid but it is variable depending on the puzzle. Now my problem is with creating the images themselves and not with the code for instance:
This is the original image:

This is one image I created within PowerPoint (because Gimp, Photoshop and Excel were a nightmare) using a square grid system:

As you can see it didn't come out so well. I suppose I need to increase the size of the grid. No problem. However, the issue became of colour bleeding, so I can blend the effect better so I decided to attempt a hexagonal grid system. And it is here I had a brick wall. See below:

The hexagonal grid is something I can't use in a table so Excel and PowerPoint are out. Gimp on the other hand is being iffy with the grid layer and filling in colour so at time an attempt to fill one cell renders most of the image in that one colour. odd.
Additionally, it isn't as user friendly. Heck paint would do the painting better in terms of ease of use but it doesn't allow layers or backgrounds so I have no idea what I'm actually creating.

SO, my questions are

  1. Is there a much simpler way of doing this?
  2. How can I fix the hexagon issue?

Any and all ideas are welcome!

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