Think you can do what you want or at least a reasonable facsimile thereof w/ basic 'TeX' interpreter -- 'LaTeX' is such a pain to deal with I'd not mess with it unless run into a real show-stopper without.
But, as far as the size, color, etc., see the document for TeX Markup in the documentation for at the link for 'Interpreter' in text function documentation. All that works for tick labels on a tick-by-tick value in the X/YTickLabel array
Just as a trivial example:
where one sees the third tick label red and smaller fontsize and bolded in comparison to the default for the other. This is w/ defatul TeX interpreter.
As far as the thing about keeping some static label, I don't fully comprehend the intent or effect, but I'd guess what you may want there would be a text object with its specific handle to refer to as the static object instead of a tick label (which is just an element of an array on a 1:1 correspondence to the ticks for a given axis). But, as the above shows, you can do all kinds of effects thingies on those individually by setting the desired properties as interpreted text strings for any element of the array--and as the way it is effected above shows, that's dynamically adjustable simply by writing the desired array location.
BTW, retrieve and then use the specific axis handle instead of sprinkling calls to gca all over the code -- that ensures you're always programmatically addressing the axis which is the intended target instead of one the user may have brought into focus.