Hello Stephen,
Thank you so much for using support forum for the query. We recommended you to make the GIF image and put that image on Header Image from Appearance > Customize > Header Options > Header Image and from Slider Options, choose the Text Slider Mode. After that, the background image will behave like the sample slider and the text on the slider only slide.
Please try once with this method. If you need the exact design above link, you need to customize the theme as your requirements.
Let us know the result.
Warm Regards
Acme Supports