How to call .ajaxStart() on specific ajax calls

2018 NOTE: This answer is obsolete; feel free to propose an edit to this answer that will work.

You can bind the ajaxStart and ajaxStop using custom namespace:

$(document).bind("ajaxStart.mine", function() {
    $('#ajaxProgress').show();
});

$(document).bind("ajaxStop.mine", function() {
    $('#ajaxProgress').hide();
});

Then, in other parts of the site you’ll be temporarily unbinding them before your .json calls:

$(document).unbind(".mine");

Got the idea from here while searching for an answer.

EDIT: I haven’t had time to test it, alas.