Try to experiment a little bit. Select your vertical profile curves, then instead of selecting all four horizontal curves, try just the top and bottom ones and see if that works. If that doesn't work, you could do multiple birails (i.e., after selecting the four vertical profile curves, select the top two horizontals for your rails, move the resulting geometry out of the way....then repeat using the 2nd and 3rd horizontals, and finally, the 3rd and fourth. Then, just attach each piece of resulting geometry. I'm assuming your vertical profile curves have 4 cvs each snapped to each horizontal curve.
"Terminat Bora Diem, Terminal Auctor opus."