The above suggestion (for padding-top) was overridden by something that changed padding-top to 73px.
<div class="stat_content_inner" style="padding-top: 73px;">
I had to add the padding-top to the inner .center instead:
.stat_has_img .stat_content_inner .center {padding-top: 250px!important;} /* added to push text content lower in the static image */
This is in addition to making the min-height larger:
.stat_has_img .stat_content_inner {min-height: 510px;} /* changed from 250 to 510 */
Kudos to layerthemes for the incredibly fast and reliable support. I am definitely upgrading to Pro. Thank you!