Used to do mold remediation work, along with lots of other stuff, and your mold will not go away until you get your R/H down. There are air exchangers with heat reclamation devices available from a variety of vendors, Honeywell makes quite a few.
The danger with attic moisture is that most homes have fiberglass, rockwool or cellulose over the ceilings, and none of these respond well to getting wet. When excess moisture builds up you get the same type of event that you're experiencing on your walls because of the temperature differential and the dew point. This is why vapor barriers are such a critical part of the construction process in New England for example. If the dew point happens to be in the middle of your attic insulation then your insulation gets wet, compacts, looses its micro air layers and compacts...further exacerbating the problem. Then you've also got the mold issue. Mold needs food, any organic matter, and moisture. Take one away and it can't survive. Typically below 40% R/H will do the trick.
Duns warnings regarding the super saturation of the air is very real. I use a wood stove in an adjoining room, rigid foam insulation over all of the windows in the fish room, and circulating fans with cross ventilation pulling air through the room and into the rest of the house. I'm just lucky that it's all in a precarious state of equilibrium, but if my dehumidifier pump drain clogs the condensation event occurs very rapidly.
My only choice at this point is to add another dehumidifier to keep up, but I've got about 2,000 gallons of aquariums to contend with too.
I paid about $200 for a dehumidifier with a built in drain pump and digital R/H and temp guage that would work great IMO. Adding heat is going to be a necessity as well however. Get the moisture down and the temp up.