Sounds like you have stone and concrete foundation walls (not clear if stone is stacked stone wall or bedrock), so maybe no accessible air vents or windows. With access through screened vents or windows into the basement for the concrete chute, assuming the concrete truck can get right to the house and that there is a door that a small conveyor or wheelbarrow can use for access, you might get this done for about $250 for the excavation, and about $750 for the vapor barrier and concrete. This assumes the foundation concrete or bedrock continues below the planned slab base level, and that the 1 foot of excavation is "dirt", not bedrock. If bedrock excavation or they have to cut a wall opening to remove the dirt by conveyor, then probably more like $500-1000 for the excavation, depending on hard the bedrock is. Remember, to drop the floor 12 inches you will need about 20-24 inches of excavation, to leave room for the bedding material and the slab plus the 1 foot of extra headroom you are working for.
If the existing foundation does not extend at least 12 inches below the planned excavation level, then this would not be a good idea, as you will be undermining the foundation wall support, unless you can tolerate a high "curb" around the outside of the slab about 1' wide and 1' high above the slab, which would be a reinforced edge to brace the foundation wall, then the remainder of the slab inset below that. This would have to be professionally designed by a civil engineer to support the foundation correctly during excavation for the slab, if needed.
Don't forget ventilation if you are planning on making this a usable space, and of course consider if the area has ever flooded in spring or after rains - that might totally change the plan, particularly with the stone walls. Remember, putting in a slab will NOT stop groundwater inflow without also installing drainage tiles or pipes and a sumpp pump before the slab goes in.