How do I accurately detect overset contents when using tables?

Question

Hello, all. I am familiar with how to detect overset contents of a text frame, namely:
if ( myTextFrame.parentStory.contents.length > myTextFrame.contents.length) {
  alert('There is overset text');
} else {
  alert('There is no overset text');
However, the contents of my story are three tables, rather than text. Each table contains dozens of cells filled with text. Yet the "length" property of the frame is only 3! How do I accurately read the length of the content given that most of it is in tables so that I can test for overset text?
In case it helps anyone, a more detailed description is:
If there are three tables in the story, and only 2 fit on a page-sized text frame, the length property of that frame will be 2. Kind of weird, but not a problem yet.
In the same scenario, however, if the third table BEGINS on the page but spills over (creating an overset situation), the length property of that frame will be 3 -- causing the test think there is NO overset text! InDesign simply sees 3 characters in the story, and only 3 characters on that page.
When I look at the "contents" property of the story, it just reads 3 squarish characters. They're obviously some kind of special character. InDesign apparently takes the concept of "table" and just writes a placeholder character for it in the "contents" property.
Am I going to have to create some routine to loop through every cell of every table and somehow add it all up to get a proper length? How do I just test for overset-ness?
Thank you!

Answer 1

Actually, Harbs, I'd already just burst my own bubble by running additional tests! So I have to revise my whole set of instructions.
IGNORE EVERYTHING I WROTE ABOVE.
Here is the revised solution, based on the initial solution proposed by Dirk and then revised to work around Harbs bug discoveries. It is essentially a corrected version of Dirks line. Instead of saying:
app.activeDocument.stories.item(0).tables.lastItem().cells.lastItem().insertionPoints.last Item().parentTextFrames.length
you would say:
app.activeDocument.stories.item(0).tables.lastItem().cells.lastItem().parent.parent.insert ionPoints.lastItem().parentTextFrames.length
That's just the short version. Here's the full code and explanation:
Summary of problem:
InDesign treats a table as a single special character, so it does not accurately report the "overflows" property of a text frame containing a table which spills beyond its margins. A text frame will show as not overflowing (i.e. myTextFrame.overflows will return false) if its final table simply begins within its margins--even if most of the table spills well beyond the text frame. So a ten-page table that starts on page one will only considered by InDesign scripting as being one character long (and therefore shown as fitting completely in first frame even when it doesn't). The solution for this, as discovered by Dirk, is to test whether the final cell of the table is in an overflow area.
The solution:
You cannot just test whether the cell is overflowing, or whether the parent text frame is overflowing, because InDesign will misreport them and their contents when they are in an overflow area, making it impossible to distinguish a cell overflow from a containing-text-frame overflow. So we just check the parent text frame of the final insertion point, which is after the last table, and see if its length is zero (meaning has no visible contents). If so, the insertion point is in an overflow area!
So the test to run is this:
var finalCell = myTextFrame.parentStory.tables.lastItem().cells.lastItem();
if(finalCell.parent.parent.insertionPoints.lastItem().parentTextFrames.length==0) {  ...your code here...  }
Of course you'll replace myTextFrame with the one you're dealing with in your own script.
Example usage:
This is how I implemented this in my own script. I have an array of text frames which I pass to this function, and by the time I call the function this array contains only one element, just the first large text frame (with my long table already placed inside it). It also relies on a helper function drawTableFrame which is simple and I'll leave out; it just adds a text frame to the new page and sizes it. And of course myDocument I've long ago set to be the document I'm working in.
// Takes array of text frames, checks for overflow, and adds pages as needed
function addOverflowPages(whichFrameArray) {
    var i = 0;
    var finalCell = whichFrameArray[0].parentStory.tables.lastItem().cells.lastItem();
    while (finalCell.parent.parent.insertionPoints.lastItem().parentTextFrames.length==0) {
        i++;
        var newpage = myDocument.pages.add(); // add new page
        whichFrameArray.push(drawTableFrame(newpage)); // draw new frame
        whichFrameArray[i].previousTextFrame = whichFrameArray[i-1]; // link new frame to previous one
I hope this one is solid at last. I have tested it with empty final cell, full final cell, partially-overflowing final cell, and totally-overflowing final cell, and they all work for me. Thanks again to everyone for pointing me in the right direction!