My house was self built 23 years ago and I did make a sump provision but never needed it.
This spring something happened as a vein opened up somewhere and I now have a pump that needs to run about every hour or so.
I'm OK as the foresight and provisions handle the present situation.
My concern is a power failure situation as we do have our fair share.
If I'm home I can fire up the genset to handle that.
I don't wish to upgrade to an automatic genset due to costs so am studying alternate solutions.
I might go battery with a 'tender' as well as a 12 volt pump.
It so happens that I have a 12 volt RV pump on hand but need to look up the GPM specs.
The battery and tender charger is no problem as I have both of those items.
Much the same as what happened to us, but the cause was a flood and ther re-routing of a local stream. About 4 years ago our water table raised so we had to have the sump pump running every hour to keep from having water in the basement. Ours is not a completely sealed traditional basket construction basement; ours is made of deep perimeter walls that go down to bedrock and then the basement backfilled with dirt. Apparently the seal to bedrock is not perfect everywhere. But when we built it that was a drainage advantage. It didn't become a problem until the water table rose. Anyway, we ended up with the same concerns you have about power and two more thngs you might not have thought of.......one being that that we were going through a lot of pumps, and the second being that we got tired of listening to the pump cycling every hour.
We eventually found a better brand of 110volt pump and also put in a second sump. Solving problems with back up systems isn't a true solution but it worked for awhile. Doing that still left us vulnerable to power outage, the pumping noise, and the energy cost. Also, the better quality pumps lasted longer, but not forever.
Two years ago I finally put put french drains on each side of the foundation walls. The french drains along the inner walls of the foundation were at at level lower than the bottom of the sumps, and gravity along drained all these french drains into a single "master sump" out out in the yard at the lowest elevation still conveniently close to the house. The master sump then drains by gravity through underground pipes going to a creek a few hundred feet away.
The whole project was labor intensive, but not much for materials. The total drainage rate at the creek outlet is about 5 gallons/minute and entirely by gravity. The drainage slope varies, but is alway between 1 and 2 %. That's is a drop of about 1.5 feet in every 100 feet.
That's not much drop, but it's all we have available. I surveyed really carefully to find it. The problem the OP has is that he has even less slope available.
good luck,
rScotty