Nice job, great to see some of these retro units being brought back to life.
The furnace could need a new sail switch, also look for a shut off valve that may be closed. If you have a little guy RV repair shop in your area he would be the guy to go to. We have a guy locally that can tell you exactly what the problem is before you can explain what the problem is.
I feel for your buddy it makes one wonder how a company that treats it's customers that sh|!!¥ can stay in business. One thing that I have found to be a serious problem in todays campers is the electrical systems.
The workmanship on the electrical systems is beyond poor, I have gone through and repaired all of the splices and Marettes in my rig. It never dawned on me that I needed to get in back of the converter, a couple of days back I opened up the cabinet that housed the converter. What a mess of wires shoved in how ever they fit, I brushed against a wire and there it goes popping out of the ground block. I don't think the set screw had seen a screw driver during construction.