Thanks everyone for your replies. I'm posting to clarify a few points since I co-own the house with Annie. She has done a great job describing our issues and getting this started, and thank you so much to all for your varied and informed opinions. We are new to permies, but feel like we belong here.
1. "your nearly 200 year old house did not always have this problem, so what has changed? has anyone around you been drilling(water, fracking, etc.)?" - well, we don't know that it has not always had this problem. Specifically our basement floor is sandstone bedrock with dry stacked rubble foundation, topped with barnstone and huge sill timbers upon which the house is framed. I see water coming in when it is wet outside. it comes in along the North wall between the sandstone bedrock and the first course of stones. We don't often see water actively entering the basement space during times of low precipitation or during periods where precipitation is frozen and stay on the surface. There is a shallow channel "dug" into the sandstone to guide this water diagonally to a corner of the basement which is lowest and serves as a mini catch-basin, equipped with a sump pump. The water is intentionally directed to this area, and has been for >18 years. We know the previous owners did not design it that way, and have no idea how long it has been that way. Could be since the advent of sump pumps, and before that someone may have used a bucket. That said, it does appear that our ability to control the mold is not as good as previous owners. This could be attributed to their willingness to use harsher chemicals (we mostly use vinegar and homemade non-toxic cleaners), their use of A/C during the summer which dries air out, etc. Last year was an uncharacteristically wet year in our area, and that may have led to an increase.
2. "if your water is coming from below grade (I feel that this is your problem) then you will need to address that with diversionary tactics once the source is identified. I see 3 possible sources; the stream, the pipe or groundwater." - Annie's earlier reference to a stream running under our house was in reference to the above-described water diversion to a sump pump area. We do also have a stream on the property (more like a ditch that dries in the summer and is wet otherwise) to the north of the house, maybe 150', and most of the surface water drains that way. However, the bedrock is shallow, about 5-6' below grade. I tried to pound a ground rod in for the electric fence and had to pound it diagonally to only leave 18" above grade. The bedrock appears to lean down hill from N to S under the house, as explained above. Though everything is worth considering, the water main installed at the street 2 years ago is not a likely source of this water IMHO since the water ingress has been this way for years. The cisterns are a possible source. I pumped them out and have not seen an appreciable increase in water returning to them. I know by inspection that there are no active connections to gutters or other pipes filling them. I also know by inspection the walls are cracked and water from moist soil could possibly enter. They are not completely sealed on top, but only have tiny 2" diameter openings so not much is entering during rains. We have well water, and the well is not at all far from our house, about 3' out from our back porch wall. The well is 70' deep into a sandstone aquifer. I know that not all contaminants can be seen, smelled, or tasted, but our water is pure, clean and delicious and we have noticed no changes in it over 5 years. While we are in an area of the country that is known for possible fracking, there do not appear to be symptoms of fracking groundwater problems and we know of no active fracking sites near us. We have not had earthquakes.
3. "probably the floor can have a drainage layer added, then a clay cap, then an impervious layer to seal ! This may be the same as adding a foot of earth into your basement, reducing your head height as much ! " - This is an interesting proposition. We are hoping to find the right people to come and see our unique, though not unprecedented, situation and provide a menu of solutions and costs that we can pick from. I can deal with losing one foot of headspace in the basement to solve dampness problems. We are starting with a home performance consultant as mentioned here, understanding the moisture may have multiple causes and certainly multiple ways to address it.
4. "So, as well as looking at the potential sources of ingress take a critical look at how you are using the space to see if you are adding excessive moisture through your patterns of use." This is a great point. I'm not aware of any changes which would lead to increased moisture. We did not start drying clothes or large quantities of food indoors. We will refrain from doing so.
5. "I meet lots of people who have a wet basement once. They ask me about the commercials they see for basement dry systems, and mostly, I steer them away. When you get a wet basement once, it's a drainage issue, and you prevent it with sensible use of downspouts. Landscaping and french drains if necessary. But what you're describing actually sounds like you might be a proper candidate for what they're selling. " - Do these systems require drains/gravel below the level of the foundation? If so, we might have the complication of our foundation being solid sandstone and extending greatly beyond the perimeter of our house, probably for miles in all directions! If water is entering between the sandstone bedrock and the rubble wall, how does one direct it away? Seal the wall to the bedrock? This does not seem feasible, but this is my first experience with a very wet basement. Alternatively a channel could be dug through the standstone bedrock and a french drain installed below the level of where the bedrock meets the wall, but that level of site disturbance close to the basement wall would make me nervous that the sandstone supporting the basement walls could crack and create some future structural problem.
Thanks again to all for your sense of adventure and encouragement.