Is there a way to re-number values in a text box, or import a list of numbers to text box?

Alternatively, this will increase every number higher than the selected number by one.

var frames = app.activeDocument.textFrames;
var x = 0;
for (var i = 0; i < frames.length; i++) {
  if (selection[0] == frames[i]) {
    x = i;
    break;
  }
}
for (var i = 0; i < frames.length; i++) {
  if ((Number(frames[i].contents) >= Number(frames[x].contents)) && 
       frames[i] != frames[x]) {
    frames[i].contents = Number(frames[i].contents) + 1;
  }
}

Each time this is run, it will increase every number by one. 

var doc = app.activeDocument;
var frames = doc.textFrames;
for (var i = 0; i < frames.length; i++) {
  frames[i].contents = Number(frames[i].contents) + 1;
}

You might want to try importing the Illustrator art into InDesign and using threaded text frames in that program for the numbers. To learn how to do this see: https://helpx.adobe.com/lu_en/indesign/using/threading-text.html.