I have a similar situation (age/ style, etc.) and am in northern NY, so similar climate issues.

I don't hold out much hope that you can successfully coat your way out of the damp-wall problem. (I've never seen anyone who has been able to do so.)

Meanwhile some questions:

Are your stones dry laid?

On my interior walls, I have the residue of frequently renewed whitewashing, which can build up and appear thick and rubbery in some places. Because it is so alkaline, it inhibits mold growth.

You can insulate the water and waste pipes and eliminate the condensate.

Do you know if your concrete floor has a vapor barrier under it? (It most likely won't if it the floor is pre 1970's....)

Have you had your cellar tested for radon?

No matter what kind of mortar you slap up on the walls, you'll still have the issue of moisture and/or vapor-proofing them.

And finally a caveat, be very wary of all kinds of proprietary basement waterproofing services' claims (both interior and exterior varieties). Many say they are a good fix, but they are more suited to modern homes with poured or block foundations. Your stones may look smoothish (or at least in the same general plane) on the inside, but chances are they are highly irregular on the outside. This not a labor saving technique; the irregularity helps "key" the stones into the surrounding earth and hold the whole thing together.

Basement dampness was not an unknown phenomenon in the mid-19th century. (Except, of course, they didn't have condensation from water pipes.) They handled this by opening ground level windows and hatches during breezy periods and backfilling the foundation trench so it drains off well. Plus, they planned for different uses than we do in these spaces; now we often have furnaces or boilers to keep them warmer and dryer in the winter which gets us thiking about year-round use. Basement conditions in our houses were/are excellent for over-winter storage of apples in barrels and kegs of sauerkraut. Nowadays we want to put in electronic machines (w/d) and recreational equipment, etc.

I have yet to vapor-barrier the floor in my main basement. It is very old concrete. My plan is to install a high-quality vapor barrier underneath a floor of rubber-zed/plasticized snap-together tiles.

I plan to whitewash my walls.

Meanwhile, I keep my stuff on shelves set-up a few inches away from the walls. I use metal shelving with the feet set down into aluminum cat food cans which keeps them from rusting.

My washing machines are up on platforms and away from the wall by by several feet.

I bought an old metal laboratory bench with a fireslate counter to use as a flower arranging surface/ workbench. Its feet are also in cat food tins.

My husband has four Stairmaster machines that live in the basement in the winter. These are parked on the floor on top of 3X6 rubber-backed polypropylene doormats.

I cannot use the basement area for storage of anything that might be harmed by higher levels of humidity: storage of Christmas things, of craft things, boxes of files, etc. These all have to in upstairs, either in closets in the living space or the attic.

And since I can not bear to have my clothes dried in this slightly musty/damp space, nor do my ironing, I have broken up the customary washer/dryer pairing.

I have a small room on the first floor that I use for drying (by machine), sorting, and mending clothing and textiles. I keep my sewing machine in this room. Since, I line dry outside almost exclusively, taking the clothes up one flight is a given.

I find that it is very useful to confine the wet part of laundry (including a capacious sink area for soaking) in the same space with a rather grand utility sink and drainboard and the watery mess of flower arranging and houseplant fussing.

Except during extraordinary times, we don't run dehus continuously, although they can dry things out nicely, in the short run. But they are expensive and noisy.

A little frank conversation with PO, might give you an idea what they tried, and how it worked, saving you repeating the same trials.

I'm afraid I have concluded that if I really wanted a dry basement, I should have bought a modern facsimile of my house, with a poured, insulated and vapor-barriered foundation. Good luck with yours!

Molly~