The problem you describe is a classic control system theory problem and is called by many names. The one I have been taught is "limit cycling". It is caused by having a system in which a decision (say to turn on a pump) has the same threshold whether the parameter (the water level) is going up or going down. The cure to this situation is to introduce a feature called hysteresis. Hysteresis is simply a concept to make the decision threshold different going up than the threshold on the way down.
Easy to say, but how do you make "hysteresis"? Depending on your background, you might see this solution in different ways. If you are seeing the world through a mechanical engineering shaped filter, you might come up with a lost motion linkage to introduce hysteresis. I would expect that there is probably some sort of hysteresis already built in to the float switch you have. One neat way is to use a mercury switch with a curved tube to hold the mercury. Because I have been trained in electrical engineering, I would use two switches, one for the high level (turn on) and one for the low level (turn off). The separation between the switches is whatever it needs to be for the particular installation. A 2 pole 12 volt relay is required to provide the logic for the switching. Simply, the relay coil is energized when the level of the water has reached the higher switch. The pump is connected to one of the contacts of the relay and will start up. The coil of the relay is "latched" through one of its own contacts and the lower level switch. When the water reaches the level of the lower switch, the relay will will unlatch because the lower switch opens the circuit to the relay coil and the pump will stop.
No extra pump, no check valve, just a little circuitry. If in the unlikely event that my explanation is not crystal clear

My Gosh, it is cold up here. Can't wait for Spring!!! I hope it is warmer where you are.
Happy pumping
Joe Mac Phee
S/V Iolanthe
CD-30 K
jvmacphee@aol.com