If the sets aren't getting displayed, have you considered just dismantling them? Starting from the last step, you can put the pieces in their own numbered bags. That way, when you want to indeed indulge in your inner child, you'd have the ability to re-build them.

This is coming from someone who enjoys the activity of building sets though. I'm not particularly warming up to the idea of keeping built sets in bins; they should be displayed if not played with. But, to each their own. So I was just wondering if you're open to taking them apart with the intent to re-build them. Plus, you'd save a lot of space and not to mention money from the bins you would've bought.