New concrete floor on wet bedrock
I live in an old New England house with a fieldstone foundation on a gradual hill. In one corner of the basement there is exposed bedrock. Whenever it rains, water flows in on the bedrock, across the sloped concrete floor, and out the door at the downhill side of the basement.
The floor of the basement slopes, but on average there was about 5 ft between the floor of the basement and the ceiling. I decided I wanted more headroom, so I've dug down the floor of the basement in half of the house. I dug all the way down to bedrock, and now have about 7ft from bedrock to ceiling.
Now I want to put in a floor on top of the bedrock. There will definitely be water flowing on top of the bedrock when it rains, so I have to take that into consideration when putting a new floor in. Everything I've read says 4 inches of gravel, then 4 inches of concrete. But then my 7ft of headroom will be decreased to 6'4" of headroom.
Is there any way I can put a floor on the bedrock that will be long lasting, dry, and less than 8 inches thick?