Adam:
You don't say what version of MathJax you are using. In v3 and v4, there is already \mathbfsfit, but it don't affect lower-case greek. With a little work, that could be handled.
If you are using v2, then the default MathJax-TeX font doesn't include bold-italic sans-serif characters, so you would need to use SVG output (or HTML-CSS, though that is the oldest and most fragile output format) with one of the fonts that do include those characters, e.g., the STIX fonts. It would be possible to define your own version of \mathbfsfit that sets the math variant to sans-serif-bold-italic, but before I spend time writing anything, I would like to know the version you are using, so I can give you the correct code.
Davide