Should I use a float "piggy-back" sump pump switch?
As kkeilman points out, your pump is fully submersible, so that part should be no problem. 

You can easily just piggy-back a float switch like this one on your existing pump. It has a special plug that you plug the existing sump pump into (no wiring necessary), and this one in particular handles up to 1/2 HP, which is more than enough for your 0.3 HP Zoeller.



The nice thing about these tether floats is you can adjust the heights depending on where you attach it, and how much tether you give it. Just be sure to test it manually moving up and down to be sure it's at the right heights, and it's not going to get hung up on anything (causing it to either stay on, or not turn on when needed). I highly recommend you secure all the wires going into the pit with zip ties or electrical tape to be sure they're not going to fall down in the future. 

You can leave the existing float working, which is fine - it will act as an extra safety to shut it off if the pit is dry, but also be sure this one doesn't get hung up - because both floats will have to be "on" to make the pump turn on -- if either is off, the pump is off.

If you don't want to use the existing float, there may be a way to bypass it internally by rewiring the pump, or you can simply zip tie it "up" so it is in the on position all the time.