Thinking about this issue the other day, I wondered if Mike could cut some pieces of wood to slide in there. Looking at the boards online, trying to find their dimensions, I thought, "They're basically the size of a plastic cutting board." A moment later I was in the driveway where I'd left the stroller after a walk, opening one of the velcro backs, and sliding a cutting board back there. Perfect.
So if you also have a 2010 City Mini, consider this solution!