I eventually got all this to work by writing client-side scripting in the afterEnterEditMode handler.  For the drop list, the script looks like:

var droplist = document.getElementById(gridName + "_vl");
if (!droplist) {
 return;
}

var r = igtbl_getAbsBounds(cell.Element, gridName, true);
droplist.style.top = r.y;
return;

For a text box that I knew wasn't multiline, I had to do:

var textbox = document.getElementById(gridName + "_tb");
if (!textbox) {
 return;
}

var seg = standardGrids[gridName];
var valid = seg.getValidationForCell(cell);
if (valid && valid.fieldLength > 0) {
 textbox.maxLength = valid.fieldLength;
}
textbox.style.height = "16px";
return;

I was a little nervous tracking down control names, since I don't think Infragistics promises not to change those control names in the future, but I couldn't find any other way to make this work.

I put the following code in the AfterEnterEditMode handler, but it doesn't seem to change anything:

var droplist = document.getElementById(gridName + "_vl");
if (!droplist) {
 return;
}

var r = igtbl_getAbsBounds(cell.Element, gridName, true);
droplist.style.top = r.y;
return;

Am I missing something? I am specifically having a problem with a WebDateChooser. I assumed that I didn't need the code below that...but should I be changing anything within the code to make it work?

The script I posted was only intended as a starting point for all the different controls that might need to be resized on a multiline grid.  In particular that code was for the DropList and the TextBox.  You would need to use the Developer Toolbar to identify the names of the other controls that handle the editing, and then figure out how to manipulate them to your taste.  I haven't tested this, but I believe the code to handle the Date Chooser looks something like:

var cell = igtbl_getCellById(cellId);
var column = cell.Column;
if (column.ColumnType == 10) {
 var editor = column.editorControl.Element;
 if (!editor) {
  return;
 }
 editor.style.height = "16px";

 var editorInput = document.getElementById(editor.id + "_input");
 var editorImage = document.getElementById(editor.id + "_img");

 if (!editorInput || !editorImage) {
  return;
 }
 editorInput.style.height = "16px";
 editorImage.style.height = "16px";
 return;
}

WOW! For not testing that, it worked perfectly! I literally just copied the code and pasted it in and it worked like a charm. Thank you so much. I really appreciate it.