For my main goal (to click on a 'hotspot' icon on an interactive page and have it bring up Sketchfab's 3D viewing window), I started off using ThingLink.
ThingLink has very few features accessible without purchasing an account ($20/month billed annually). And only the Premium version ($125/month billed annually) allows you to edit with VR features and 360 photos.
Advanced features are limited to uploading image files and audio files (as well as minor changes to the visual style of the page). I copy/pasted the embed code from Sketchfab into two of the boxes for a clickable tag:
The "Text" Box (which only showed the text of the code in the pop-up window)
and the "Link or Image Address" box. This did display the Sketchfab window, but layered it underneath the main image file (despite efforts to change the importance order of layers in the Inspector)
Ultimately concluded ThingLink is not the way to go.
Next Steps
Try another Interactive display tool
Build our own