first, I wrote below code. It is really you wanted, but I think you can reference it.

var slct = app.activeDocument.textFrames[0];
var plen = slct.paragraphs[0].length;
var hlen = slct.story.lines[0].length;
var hscale = paragraphs[0].scaling;
var step = 0.01;
while (plen != hlen) {
    slct.paragraphs[0].scaling = [hscale,1];
    hlen = slct4.story.lines[0].length;
    hscale -= step;
    }

We can detect overflows, comparing lines and paragraphs properties.

second,
We can make threaded textFrames, use baseFrame property. And normally, add to after baseFrames.
When we set postFix to true, areaText add to after baseFrame. See below.

var bf = app.activeDocument.selection[0];
var a=app.activeDocument.pathItems.rectangle (-100,100,100,100);
var b = app.activeDocument.textFrames.areaText(
    a,
    TextOrientation.HORIZONTAL,
    baseFrame=bf ,
    postFix=true
    );

*upper frame is baseFrame.

var bf = app.activeDocument.selection[0];
var a=app.activeDocument.pathItems.rectangle (-100,100,100,100);
var b = app.activeDocument.textFrames.areaText(
    a,
    TextOrientation.HORIZONTAL,
    baseFrame=bf ,
    postFix=false
    );

false mean preFix, like below image.

*upper frame is baseFrame.

OK Lionel, check below script.

//overflow control.
var counter = 0;
slct = app.activeDocument.selection[0];
cntsLength = getChars(slct);
visibleChar =getVisible(slct);
var vscale = 1.0;
stepNum = 0.02;
while (cntsLength != visibleChar) {
    scalingWidth(slct, [vscale,1]);
    visibleChar =getVisible(slct);
    vscale = vscale-stepNum;
    }

function getVisible(txObj){
    var result=0;
    for (var i=0;i<txObj.lines.length;i++){
        result += txObj.lines[i].characters.length;
        }
    return result;
    }

function getChars(txObj){
    var result=0;
    for (var i=0;i<txObj.paragraphs.length;i++){
        result += txObj.paragraphs[i].characters.length;
        }
    return result;
    }

function scalingWidth(txObj,wscl){
    for (var i=0;i<txObj.paragraphs.length;i++){
        txObj.paragraphs[i].scaling = wscl;
        redraw();
        }
    }

This time we fit contents to textFrame, press contents width.

scaling property is an array. It contain horizontalScale and verticalScale.

scaling = [horisontalScale, verticalScale] (0 to 1)

If you want set to 100% width and height...

scaling = [1, 1];

Illustrators OMV sometimes do not written I really wanted to. So I try to check properties myself.

Ten wrote.

Excellent script been looking for exactly this  for a while now. Well done mate.