I did this exact thing about a year ago, but I think it took me a couple of tries to get it right. I wish I had taken better notes—I wrote out too many calculations, but I think what worked was a simple volume ratio. You need three figures—I will assume your width and height are the same.
Original: 4 x 4 x 16 = 256
Pan 1: 4.5 x 4.5 x 16.5 = 334.125
Pan 2: 5.5 x 5.5 x 10.25 = 310.0625
Recipe for pan 1, multiply by 1.31 (round to one and a third if working by volume)
Recipe for pan 2, multiply by 1.21 (round to one and a quarter if working by volume)
Obviously, this is easier to execute if you are working by weight.