This is far from perfect yet it gets you a lot closer to what you were trying to achieve. If we make the ui-slider-handle a width of 0 or maybe even 1, you now can use that as the exact counter point. You can push the handle out with padding in CSS to make it interact-able again.
$(function() {
  $("#mySlider").slider({
    classes: {
      "ui-slider": "collision"
    },
    range: true,
    min: 0,
    step: 1,
    max: 100,
    values: [0, 100],
    slide: function(event, ui) {
      if (ui.values[0] >= ui.values[1]) {
        return false;
      }
      $("#mySliderVal").val(ui.values[0] + " – " + ui.values[1]);
    }
  });
  var sldr = $("#mySlider").slider("widget");
  $(".ui-slider-handle:eq(0)", sldr).css({
    "padding-left": "8px",
    "margin-right": "-2px"
  });
  $(".ui-slider-handle:eq(1)", sldr).css({
    "padding-right": "8px",
    "margin-left": "-2px"
  });
  $("#mySliderVal").val(
    $("#mySlider").slider("values", 0) + " – " + $("#mySlider").slider("values", 1));
});
body {
  font-family: Helvetica, Arial, sans-serif;
  margin: 20px;
  display: flex;
  justify-content: center;
}
#container {
  width: 200px;
}
*:focus {
  outline: none;
  -moz-box-shadow: none;
  -webkit-box-shadow: none;
  box-shadow: none;
}
input,
label {
  font-size: 13px;
}
div.ui-slider.collision {
  margin-top: 10px;
}
div.ui-slider.collision .ui-slider-handle {
  opacity: 0.75;
  width: 0;
}
div.ui-slider.collision .ui-slider-range {
  background: transparent;
}
<link rel="stylesheet" href="//code.jquery.com/ui/1.12.1/themes/base/jquery-ui.css">
<script src="https://code.jquery.com/jquery-1.12.4.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.js"></script>
<div id="container">
  <input type="text" id="mySliderVal" readonly style="border:0; color:#f6931f; text-align:left;width:75px">
  <div id="mySlider"></div>
</div>