Plumber Ricks first question is the most important thing we must look at given the symptoms you describe.
At first read it appears that you may need to change over to a pedestal pump where the motor actually sits well above the rim of your sump. This allows for a float to ride up and down a guide rod that is very easily adjusted for depth. The rod activates the motor which turns the pump down in the sump. You can adjust this rod to allow your sump to fill substantially before it activates your pump. Never let the water get past 1 or 2 inches over the top of the foundation drain pipe entering your sump. Your foundation drain pipes can have some water build up in them without a problem. If they sit full for a long time while water pressure builds against your floor or basement walls then you can have a problem.
The next thing we must look at is the discharge of your pump line. Does it discharge to a location that allows the water to recycle right back into the pumps sump. i.e, discharge pipe broken outside next to wall or discharges to where water pools and runs down the basement wall directly back into the foundation drain. All the different pumps in the world will not solve your problem if there is a discharge issue.
After you answer Ricks other questions it may well be deternmined that a different set up is best. But so far a pedestal pump is my recommendation.
One note: Aside from a wet floor your sump pump is there to protect your foundation and the structural integrity of your home. Hydronic pressure is one of the strongest pressures known to man. Water does not condense, therefore it can push an entire concrete floor up or even lean a home off square to where serious structural damage can occur. Please don't try to save 25 dollars and get by with a cheap pump.
My personal experience with diaphram switches have usually been negative. So there is no reccomendation from this poster concerning them other than to leave them sit on the shelf in the store.
Work hard, Play hard, Sleep easy.