This sounds awful, but I was searching the Internet for environmental enrichment ideas, and it seems that some laboratory guidelines contain useful suggestions. Getting the pigeons to forage for their food was a big one - second to free flying time, which was most important.
Some ideas I've come across: burying seed in amongst smooth river stones/shredded paper/hay or straw (clean, dust free), providing a planted grass area, a shallow bathing pool (supervised), perches of different heights (or boxes for a playpen?), providing nesting materials, changing the pen layout. My pigeon loves chasing a cat ball around the bottom of her cage, as well. Hope these suggestions help.