Thanks for all the input guys. I fully understand the risks, which is why I sought some other opinions before chopping into the floor. I hesitate to contact a contractor because they are in it to make money and will most likely dishonestly advise whatever will put more of my cash into their pocket. Approaching a contractor I do not know and offering to buy drinks is a good way to make them think I am after more than their professional services.
I do not believe there is "running water" under the floor, or else there would be a LOT more flooding than there is. It's just a matter of a saturated water table. Last year's flood was the worst I have ever seen and even then the floor drain was more than adequate to keep up with the flow coming in. It was never super bad, just enough to cover the low areas of the floor.
I also understand the risks in cutting into the floor. Any hole I create will be at least 4 feet away from any walls to eliminate the chance of compromising the structural integrity of the walls. Yeah, I don't need the basement becoming the first floor.
The sealant would be a good idea if the floor was just prone to "sweating", but flowing water is powerful stuff and it will find a way in no matter what. So, trying to block the water is probably not gonna work. Even pouring another layer of cement would be a temporary fix if that, and all I'd get out of the deal is a lower ceiling.
The idea behind the sump pump idea is to 1) drain water under the basement
before it can come in (or at least reduce the intensity), and 2) control
where the flow comes in.
I'm still doing research, but everything I've read points to the sump pump idea. It's just a matter of how I'm gonna cut the floor, which I think we've covered.