How can I handle water softener output without relying on a sump pump?
Water softeners can drain up and out. The house I currently live in has a softener drain that runs up about 5 feet from the softener and over through the basement to the drain. So, you could drain it outside fairly easily.

I have never had a problem with it but if you are concerned about drain back you can put a check valve in the drain tube at the beginning next to the softener. Mine doesn't have any and it works fine.

Good luck!