InDesign: ExtendScript to list fonts and extended font information

I need to list detailed information about the fonts used in a set of inDesign documents. The information I need is essentially accessible through the menu item Type › Find Fonts… (as explained here) but going through each font in every document and writing down the information is not feasible.

I can find much of the information in the Font objects underdocument.fonts and my question is how to access or generate the extended properties found in the panel below:

• Character count for the given font
• Pages where the font occurs

_{(source: indesignsecrets.com)}

Edit: The document.fonts array also doesn't seem to include missing fonts.

Well, here's a brute-force strategy for character counting. It iterates through every character textStyleRange in the document and checks its applied font. Edit: Updated to use textStyleRanges. Much faster than going through every character.

var document = app.open(new File(Folder.desktop.fsName + "/test/test.indd"));
try {
    var fontMultiset = countCharsInFonts(document);

    // For each font, display its character count.
    var fonts = document.fonts.everyItem().getElements();
    for (var i = 0; i < fonts.length; i++) {
        var fontName = fonts[i].fullName;
        $.writeln(fontName + ": " + fontMultiset[fontName]);
    }
}
finally {
    document.close();
}

function countCharsInFonts(document) {
    // Create the font multiset.
    var fontMultiset = {
        add: function add(fontName, number) {
            if (this.hasOwnProperty(fontName)) {
                this[fontName] += number;
            }
            else {
                this[fontName] = number;
            }
        },
    };

    // For every textStyleRange in the document, add its applied font to the multiset.
    var stories = document.stories.everyItem().getElements();
    for (var i = 0; i < stories.length; i++) {
        var story = stories[i];
        var textStyleRanges = story.textStyleRanges.everyItem().getElements();
        for (var j = 0; j < textStyleRanges.length; j++) {
            fontMultiset.add(textStyleRanges[j].appliedFont.fullName, textStyleRanges[j].length);
        }
    }

    // For any fonts that aren't applied in the document, set the character count to 0.
    var fonts = document.fonts.everyItem().getElements();
    for (var i = 0; i < fonts.length; i++) {
        var fontName = fonts[i].fullName;
        if (!fontMultiset.hasOwnProperty(fontName)) {
            fontMultiset[fontName] = 0;
        }
    }

    return fontMultiset;
}