The colors "yellow" and "cyan" are impossible to read on the white background.
May I suggest that you use class="ansicolor-cyan" instead of style="color: cyan"? This would allow someone to override the exact saturation/value of a color to make them readable.
By default, I'd suggest the following colors:
I don't have an example of all the different colors, magenta may also be a problem...
You could do this with all the various attributes, including 256 color ansi sequences, bold, underline, bright, etc.
I'd be happy to help with the CSS...