I’m almost too embarrassed to ask but I gotta learn eventually…
Is there a way to snap to or grab the 3D blue box that surrounds a selected group or component (for moving or measuring)? I’ve googled and googled…
No. There isn’t but ThomThom made an extension that draws a box the size of the bounding box. It either makes it as guidelines and guidepoints or as geometry. I use it when I need to do the sort of thing you’re trying to manage.
Check the Extension Warehouse.
And here’s the link to Daves suggested plugin:
http://extensions.sketchup.com/de/content/draw-boundingbox