It's an OLD house and old basement, and the floor is very uneven, and the water that pushes up from our very-high water level (most houses here don't have basements for that reason) tends to pool in the low spots.

Can I use a self-leveling concrete to even out the floor?

My biggest question is how do I handle it around the sump well - do I build a barrier a few inches out from it and then trowl in some regular concrete at a slant once the self-leveling has fully cured?

Also, what would be the best way to put in some kind of mini-trenches to direct the little bit of water that still ends up on the surface over to the sump well: press something into the wet concrete that I could take or chip out once the concrete cured (if so, what?)? Use a circular saw to cut out some trenches once it's dried? Any other ideas?

And just in case it's not obvious, this basement is all about function - appearance really doesn't matter. We go down there very rarely.

As far as a "trench", you probably will not be adding a significant thickness. Sections of PVC resting on the original floor would probably be the easiest method.

Good luck.