Sump pit filling very quickly from inlet pipes
To raise the float level without adding any additional points of failure, just move the whole pump up - shorten the pipe, put concrete blocks under the pump to raise it in the pit. Your power bill will thank you.

You could try putting a strong dye [food coloring or fabric dye can work, but "septic dye" is probably the most effective] in the water, though it may be hard to tell what's happening with that - I have to suspect that you may be pumping in circles (outlet insufficiently far from the house, so the "discharged' water shows up in the pit a few minutes later) but that will be tricky to trace with dye.  If all the water is "new" the dye should just get progressively paler, and the water coming in the drainage pipes should be clear, not tinted. You can also look for dye coming out into places away from the house.



A more complicated approach that might work would be to mix up or buy a strong dye solution and use a tube to "inject" it very near the pump intake as the pump is pumping (trying to minimize what gets in the sump itself) and then you might see the sump get darker if it's recirculating.

It sounds like the water may be passing in from one or more of your pipes and out again from one or more of your pipes (when the pump is not powered up) - a little bit of dye squirted near each pipe in turn (with the pump off) may diagnose this and show if there is "flow-though."