Furnace Ideas / Help

Well I am stuck. After looking at your photos and the destructions, it appears that any trap function is built in. It MAY be the white plastic fitting there where the drain connects. An easy way of handling that would be to try a very small heater right inside the furnace. One way would be either a single low wattage 220Vbulb, but operated on 120V. A 100W 220 bulb on 120 would be 25 W and last a long time, and you would not need that much. Alternatively, if you could "hack" up a couple of sockets and run them in series, this would run two 120V lamps at half voltage. If you ran a pair of say 15W or 25W bulbs (not LEDS but incandescant) that would give you 1/4 of 50W or about 15W and should be plenty with the door on.

EDIT. I was going to suggest "if you dare" to disassemble that white plastic device and see if there is a "stand pipe in there that would form a trap.