As hkmaly suggests, the trick is basically to preserve Dan's shading as far as possible whist still attaining the desired colouration and brightness.
Mainly, this amounts to significantly limiting operations on the value channel to those which don't affect the shading (applying levels/curves/gamma/contrast/etc to specific regions (usually not the entire image) is generally fine, provided this is done in such a way that it doesn't noticeably mess up the region border).
The hue and sat channels are a different matter, and can even be region-floodfilled, although I didn't have to resort to that here (I do when I'm e.g. colourising from greyscale though).
My first version basically made the hair and attire lighter in colour. The second shifted the focus to contrast and saturation, thus increasing brightness rather than simply lightness. The final effect on the second version was to take something closer to the first version, use the levels tool to extract only the highlights, blur the result significantly and then use it as an additive layer, with a certain tuned alpha, above what I had so far for the second image. This gives the image an additional subtle glow.
Use of waifu2x beforehand is also very helpful, mainly because it makes selecting regions a lot less fiddly.