I like spending other people's money. I wouldn't bother trying to get your old converter working kinda. The new ones are much better. Get it on order.
Take delivery, and have fun installing it. It is a project requiring some thinking. Old Airstream's wiring convention is not necessarily the way the converter instructions describe it. The heart of the 12v
system is the fuse box. Both the battery and the converter come into the fuse box to feed the 12v circuits to the trailer. The circuits are protected from overloads by fuses. My 66 Trade Wind had 3 12v circuits coming out of the fuse box. Study your current wiring in and out of the fuse box. Identify the function and color of each wire and write it down as well as make a diagram. Generally red is battery plus, black is 12v circuits to the trailer, white is negative or ground.
While I'm spending your money, did you get that multi meter? This is an invaluable instrument for a vintage Airstreamer.