Ok, I did some poking and found what appears to be the solution. Making these changes allows the calling functions to remain unchanged.

Old (getElementsByTagName):

function GetHeaderCells(gridID) {
    var grid = ISGetObject(gridID);
    if (grid == null) { return null; }
    // Get parent or child WebGridRow object
    //var theTable = grid.RootTable;
    var theTable = grid.GetSelectedObject().ToRowObject().SubTable;
    return theTable.GetElement(WG40.COLHEADER, WG40.HTMLDIV).getElementsByTagName("td");
}
function GetFooterCells(gridID) {
    var grid = ISGetObject(gridID);
    if (grid == null) { return null; }
    // Get parent or child WebGridRow object
    //var theTable = grid.RootTable;
    var theTable = grid.GetSelectedObject().ToRowObject().SubTable;
    return theTable.GetElement(WG40.COLFOOTER, WG40.HTMLDIV).getElementsByTagName("tr")[1].getElementsByTagName("td");
}

New (children):

function GetHeaderCells(gridID) {
    var grid = ISGetObject(gridID);
    if (grid == null) { return null; }
    // Get parent or child WebGridRow object
    //var theTable = grid.RootTable;
    var theTable = grid.GetSelectedObject().ToRowObject().SubTable;
    return theTable.GetElement(WG40.COLHEADER, WG40.HTMLCELL).children[0].children[0].children;
}
function GetFooterCells(gridID) {
    var grid = ISGetObject(gridID);
    if (grid == null) { return null; }
    // Get parent or child WebGridRow object
    //var theTable = grid.RootTable;
    var theTable = grid.GetSelectedObject().ToRowObject().SubTable;
    return theTable.GetElement(WG40.COLFOOTER, WG40.HTMLCELL).children[1].children[1].children;
}

Of course, I'm worried about the possiblity that I got the right answer from the wrong place, so if you could confirm that what I'm going to use is stable, I'd appreciate it.

Sorry about that. You can remove the .js references and add this at the beginning of the <script> section:

        function OnAfterInitialize(a, b, c, d) {
            var grid = ISGetObject(a);
            if (grid.RootTable.GetRowsCount() == 0) grid.ResetStatus(true);
        }

 Thanks!

(Sorry for the delayed reply... I didn't realize I needed to turn on reply notification)

The suggestion for using SubTable helped a lot! I can iterate through the rows. But I can't seem to find the cell where I need to update the total.

In the snippet below, I'm able to iterate through the rows by substituting the SubTable object for the RootTable object:

var grid = ISGetObject(gridID);
// Get parent or child WebGridRow object
//var theTable = grid.RootTable; // parent
var theTable = grid.GetSelectedObject().ToRowObject().SubTable; // child
var rows = theTable.GetElement(WG40.BODY, WG40.HTMLTABLE).getElementsByTagName("tr");
// iterate through all rows
for (var i = 0; i < rows.length; i++) {
   if (rows[i].type == "Record") {
      sCellValue = grid.GetRowByElement(rows[i]).GetCell(columName).Value;

With a similar substitution, I'm able to correctly grab the index to the header column. The GetHeaderCells function returns an array of 20 columns, and my "Percent" column is [7]:

headerCells = theTable.GetElement(WG40.COLHEADER, WG40.HTMLDIV).getElementsByTagName("td");

But something's wrong with the code that's supposed to get all the footer cells. There are only 2 elements returned by this call, and neither is my "Percent" column:

footerCells = theTable.GetElement(WG40.COLFOOTER, WG40.HTMLDIV).getElementsByTagName("tr")[1].getElementsByTagName("td");

I suspect I need to be looking somewhere other than row index [1]... but where?