kp, you mention a sump pump has been installed. Do you mean the sump was added to the existing home, or was put in when the home was built? Does it run often during these wet periods?
If the sump is original, and it isn't filling and draining with rains, it's likely that your drain tile which feeds the sump has silted at least partially closed. Some companies like Roto-Rooter now have a fantastic drain tile cleaning system which clears clogged drain tile very well.
If your sump is filling and seems to work hard during rains, and your water problem is visibly coming from an area or two that are across the house from the sump, it may be clogged and treated as above, or, your drain tile may not have been properly installed. I have found a few homes in the past where the drain tile was supposed to go through an interior footing, but instead the installer had gone over top of the footing and stomped it flat so that it didnt stick up through the basement floor. This acts just like a plumbing trap, and the water level must rise into the floor before it can get to the sump, if it can at all.
P.S. Bravo for having the good drainage and spout extensions!