You will no longer be balanced and your CoM will shift too much to your outside ski, resulting in you flattening and coming out of the turn. The reason is because, assuming the same forward velocity, the shorter radius skis creates a higher amount of centrifugal forces due to faster rotational velocity - you are balanced because by placing your CoM over your outside foot, you are able to resist the inertia to travel in the straight line (i.e., tangentally) caused by your constantly rotating vector caused by your carve. On the longer GS skis, your rotational velocity is drastically reduced, nearly eliminating your lateral inertia and tangential vector, resulting in an absence centrifugal forces. The amount of pressure you place on your outside ski will greatly surpass the centrifugal force available from your turn, and so you will simply stop turning and find that you are excessively balanced over your outside ski.
Close, good try. You nailed the forces involved, you just got the effect reversed.
Yes, the slalom ski does produce a sharper turn and therefor higher centrifugal force, just as you correctly pointed out. To stay in balance when those forces are trying to eject us to the outside of the turn, we must move out Center of Mass (CM) towards the inside of the turn. If suddenly those centrifugal forces were removed, we would be rendered instantly out of balance, with our CM too far inside our feet, and we would hit the ground.
Same thing happens if the Centrifugal forces are reduced, such as you pointed out happens when a slalom ski is magically changed into a GS ski. We are again rendered out of balance, with our CM too far inside our feet. The state of imbalance is just less severe than when centrifugal force goes away completely, but we still begin toppling towards the inside of the turn, until we do something to save ourselves from an eventual rendezvous with the snow.