Sounds like you have a two part problem.
If there were a lot of rain and the ground was saturated the pit might work like a regular sump pit to keep water from coming up though the floor. This would be a good thing. But- you can't pump this volume of clear water to the septic system. I think you need to live there longer to really see how much ground water is coming in when things are seriously wet out. You might need that sump pump.
If that is the case, your laundry should run to a separate basin that is hooked to your septic system. You should also consider that lint from a washing machine will greatly shorten the life of a sump pump. Grey water should be pumped with a pump that is approved for solids.
Meanwhile you might consider using some of the natural enzyme products that are used for septic maintenance. A small dose in the pit may take care of your smell. In a place with city sewer, bleach is king.