Unlike a thermos bottle, living environments need one air change per hour. Sealing off the space, then burning a fuel that contains some water will add humidity to the space. Running the de-humidifier partially solves the problem as you found.

Add some air flow, stop heating the entire space and use pipe heater cables under the new pipe insulation. This method is a lot cheaper than adding heat to the whole space and keeping that dehumidifier running.