I'm sure glad you got that furnace issue resolved. I've been following along - it's been a long time that you've been dealing with that.
When we had that same trailer, we had problems with the sail switch and decided to fix it ourselves.
I found the wiring was too short to pull the furnace out of the cavity, so we had to change it out. This was much easier than I first thought. We installed new wires and included a Molex-style plug at the furnace side so it can be unplugged and taken out if ever needed in the future.
And yeah, we didn't use wire nuts to connect the wires
After that was done, we never had another problem with the furnace. It was so nice being able to depend on cabin heat when it was cold out!