How to display data label inside HTML5 progress bar? (cross-browser)

All you need to do is set the status text to have a z-index of 1 (-1 is invalid, 0 is the default) on the status text element and then set a negative margin-top: -32px (for a height: 32px) and you can keep the progress element without adding any excess:

<div style="z-index: 2;"><span>Staging item 144 of 271...</span></div>
<div style="margin-top: -32px;"><progress max="100" value="44">44%</progress></div>

TL;DR: Don't use pseudo elements on a <progress> element.

As said in other answers, and by me in the comments, a HTML/CSS progress bar would be a better solution than using the <progress> element.

Gecko-based browsers, like firefox, won't display the pseudo element at all.

However, to answer your question, just position the text over the progress bar:

progress {
  text-align: center;
  height: 1.5em;
  width: 100%;
  -webkit-appearance: none;
  border: none;
  
  /* Set the progressbar to relative */
  position:relative;
}
progress:before {
  content: attr(data-label);
  font-size: 0.8em;
  vertical-align: 0;
  
  /*Position text over the progress bar */
  position:absolute;
  left:0;
  right:0;
}
progress::-webkit-progress-bar {
  background-color: #c9c9c9;
}
progress::-webkit-progress-value {
  background-color: #7cc4ff;
}
progress::-moz-progress-bar {
  background-color: #7cc4ff;
}

<progress max="100" value="50" data-label="50% Complete"></progress>

Note that this does not have good browser support(In fact, it's pretty horrible), because <progress> is a replaced element, like <input>.

The CSS specs are not completely clear on if replaced elements can have pseudo elements, so different browsers have different renderings. Webkit-based browsers, such as Chrome, will sometimes display them. Gecko-based, such as Firefox, will not.

See this answer on a somewhat similar question.

So, if this is for a website, and not a electron app or similar, I highly recommend using a HTML/CSS Progress bar:

.progress {
  height: 1.5em;
  width: 100%;
  background-color: #c9c9c9;
  position: relative;
}
.progress:before {
  content: attr(data-label);
  font-size: 0.8em;
  position: absolute;
  text-align: center;
  top: 5px;
  left: 0;
  right: 0;
}
.progress .value {
  background-color: #7cc4ff;
  display: inline-block;
  height: 100%;
}

<div class="progress" data-label="50% Complete">
  <span class="value" style="width:50%;"></span>
</div>

Note: Even if this is for an application with a webkit-based browser, you still shouldn't use psuedo elements on a <progress>. As I said above, the specs for this functionality are unclear, which could change in the future, breaking your progress element. Webkit could also drop support for this.

I would recommend just using a HTML/CSS progress bar, you'll save yourself a lot of trouble in the future.