My house is situated on a lot with a walk-out basement and down sloping back yard. Could I build a tub like structure above the existing sump well with a drainage pipe running out the back foundation wall (above grade)? This would contain potential overflow and allow it to run outside naturally.
It is possible that (using trial and error) you keep getting water seeping up onto the far side of the basement floor unless you keep the level in the sump pit below the level of the 3 inch or 4 inch drain pipes that empty into the pit. In that case you will never get the level high enough to flow out over the bathtub like structure that you built atop the pit.
Each time you want to change the float settings on the sump pump, allow ten days before drawing any conclusion as to how well it worked.
Don't let the weatherman string you along. Stick to your lawn watering schedule until it actually starts pouring.