Well this method worked for one of these instances, however I still find myself unable to select an animation I have positioned in the background, namely a BB_BASE_PISTON.
I've even tried selecting the entire map, with all layers visible and selectable, and moving/deleting it all, and no luck. The animation remains firmly placed in the background, unable to be moved
It's not the biggest issue ever, as I've covered it with a texture but I'd hate for others to encounter this issue and end up ruining the visuals for their map as a result.
I wish I could be more help in working out how this issue came about. All I remember is picking out an animation, positioning it in the background using parallax and turning the speed up to 100 (so that I could see the animation play out). I then moved on to work on something else, and when I returned to turn the speed back down to 1, I found I could no longer select the animation.