(despite the sump "pit" not being quite deep enough for my liking) .
I suggest a pit with at least 3 cubic feet (a little over 20 gallons) below the rims of the perimeter drain pipes. An 18x18 inch square pit (clear space, not counting a brick lining or gravel fill) would need to extend 16 inches below the drain pipes. The pit may be close to the wall even though it is much deeper than the foundation footings.
This allows longer pump run times and fewer on off cycles. This allows more time for already accumulated water in the drain pipes to make its way to the pit before the pump shuts off, if the turn on level was a bit above the drain pipe rims. This reduces the impact of water in the outlet pipe falling back down if the check valve did not seal completely.
Tornado victims: Do not rush to rebuild. Take your time and look for and get a good contractor. Or consider selling the property and moving to a home that is ready to live in.