Well now I am really shocked.
Decided to do a factory reset yesterday. Had it over two years and it's never been done, so thought it was time. Backed all my stuff up, then did the deed. Was pleasantly surprised to see when it had finished that Google restored a great deal of my stuff automatically. No problems.
Spent the morning with the device, and had been thrilled at it running so sweetly. So with a quiet morning at hand I decided to manually restore the few missing apps and games.
Come to the device tonight, and WTF?? It's running like absolute dogshit. How has this happened? I don't get it. I'm not running anything questionable, nothing sideloaded or dodgy. But trying to multi-task is impossible. It's struggling with one app, but have two or three running and it is impossibly slow and impossible to use.
So I've already cleared the cache partition, I've already factory reset the device. There's too many theories and solutions for this problem on the net so it's difficult to find the cause. However I think it's simple - Google cannot have tested Lollipop properly on the 2012 Nexus 7. I read there's version 5.1 coming soon. It had better be bloody quick, and it had better be fixed.