I did like "Done That" and had the same results -- A sump pit and sump pump, in my case in the lowest corner of the basement. You might want to have someone who knows a little about the local water table characteristics to give you advice. I was told that in extreme cases, hosues with concrete foundations and floors have litterally been shifted (raised, usually not evenly) by high watertable levels.
Lowering the water level under the house enough can stop the seepage through the cracks in the floor. Seepage through the walls may or may not occur in association with the water table. Walls can leak when water works its way down from the surface to the watertable, even when the watertable is well below the floor level. An elevated water table can leak not only through the floor, but also through cracks in the wall.
Water table issues may not respond to corrections in grading, getting down-spout water away from the foundation, or or newly installed outside "weep" drain systems. Where my grandmother lived, the floor was poured almost directly on bedrock -- they actually blast before putting in basements. In this environment, the water table behaves differently than where I live -- which is on a glacial moraine. Water tables also can be affected by nearby lakes and rivers, outside flooding, new nearby construction, and other things.
If you can keep up with the water now -- while water tables are high, the floors will probably dry out in a few days or a week or so when the watertable goes down again. Don't think things are "cured". It will happen again when the water table returns