Pixel precise hexagonal filter?

I'm as green as it gets with this software (bought it a few hours ago), but it seems like my best bet for achieving what I'm trying to achieve.
I need to take an image:
(abstract example)

and filter it such that it becomes a bunch of hexagons:
.

As you can probably guess, I've already used the software to kind of sort of accomplish this.
The problem is that I need more precision/consistency. The filter I use in the above example (Filled Hexagonal Tiles, by uberzev) isn't quite precise enough.
I need the hexes to be the exact same height and width in pixels.

Could I use the sprite as some kind of mask? How could I accomplish this? Thanks in advance.

I was working on this when Ramlyn replied. I squashed the input image then un-squashed it. Repeat H and V must be equal for this to work. For FF13 and above.

Filled Hexagonal Tiles square hex (1).ffxml

For the issue where you say "I need the hexes to fit in exactly with the red grid", there is surely a solution.
You can use two Bomber components with similar settings. The first to generate the image made of hexagons and the second to generate the grid. If the two Bombers have the same settings, they should match and you will not have the difference that you showed in your picture.

Instead for your sentence "This is the filter without anti-aliasing. For whatever reason, the hexagons aren't at an even size to begin with, so scaling them only partly solves the problem". I also saw this problem sometimes. I think this is the reason why we have the anti-aliasing.

Maybe, if you post your filter here, we can try to find a way to get a good result.

I notice that even the built in Tile function has issues if the mortar is thin - and I don't think there is an answer.