How can I replicate the style of images produced by an old Finepix digital camera?

Question

I've got some old photographs taken by a FujiFilm FinePix S602Z. I'd love to stylize new photos (taken by a current higher quality camera) to look in the most similar way. What's the correct approach to achieve this?

Notes:

1. Colours: The S602 images have had a specific tint/hue. The sky was a sort of faded turqoise, tree leaves less saturated etc. New photos need to be tone-mapped via a histogram/curve/? in that way. How do I get the correct parameters?
2. Pixel Rendering: Super CCD sensors - thanks to octagonal pixels scanned diagonally - produced specific object edges.
3. Adding some noise and a bit of chromatic aberration is no problem for me.

Sample FinePix S602Z photo showing the specific sky colour and pixel rendering (see tree leaves at 1:1 in the Original resolution).

My own unprocessed samples - both native sensor 3.1Mp and camera interpolated 6.3Mp uploaded here. Please use the Download button above to get them in the full resolution.

Answer 1

This is my best I can do at the moment but I don't accept this answer as it's only at a halfway to desired results.

Software used: SilkyPix; GIMP 2.8 with GMIC, Focus blur and Color packages.

Pixel Rendering

1. Develop the current camera RAW with no corrections.
2. Scale the image down to sensor size (2048x1536) with No Interpolation.
3. Apply Focus blur with the Radius = 0.3 and defaults in other setting
4. Apply GMIC->Degradations->Noise [additive], Amplitude = 6, Channel = Saturation.
5. Filters->Colors->Chromatic Aberration, Lateral Blue = +2, Red = +1.
6. Layer->Rotate 45 deg. CW
7. Scale to 2832x2128 target image size with No Interpolation
8. Layer->Rotate 45 deg. CCW
9. Flatten Image before further processing
10. Apply Unsharp Mask with Radius = 1.5

Colours

1. Filters->GMIC->Colors->Tone Presets, Velvetia, Strength = 100
2. Colors->Hue/Saturation, Hue = -15, Saturation = -30
3. Colors->Curves, clip highlights on the sky a bit

Store to 4:2:2 horizontal JPEG with target size of about 2 MB (quality = 96).

Original (current camera) image (downsized)

Degraded (stylized) image (downsized)

Degraded (stylized) image rendering detail

Original FinePix S602Z rendering detail