I wouldn't have made this suggestion prior to last night, but have you considered using the F cabin?

I only say this because there was a dog loose in the first class cabin on the EWR-PDX flight. I guess his owner fell asleep while he was out of his carrier. He ran around for a few minutes through the aisle and under a bunch of the seats before the FA noticed and was able to collar him and wake up the owner. That was the first time I'd seen that.