Hello Thill, welcome to all things Airstream. I see you are from the heart of RV manufacturing in this country. I'll bet your friends and neighbors are good sources of information and parts.
I installed new gray and black tanks under my 66 Trade Wind. It was a major project for me. I felt a gray water storage tank is required if you plan on traveling in your vintage Airstream. A "tote" tank as another alternative.
The belly pan comes off as well as the old insulation. While I was at it I cleaned and inspected the frame, then I painted it so it will last a little longer. I elected to hang my new tanks from the frame rails and drain the tanks from the street side below the frame rails as is the convention on most newer trailers. The toilet sits over the black tank of course, but I had to relocate the toilet.
I ordered my tanks from Inca Plastics in California. The tanks are about 26 gallon capacity. I also used their rubber grommets instead of spin welding threaded fittings to the tank. This allowed a bit more flexibility in running the drain and vent lines.
Here is a photo of the two tanks I purchased from Inca Plastics, then a photo of the tanks installed under the trailer subfloor, then a photo of the tank drain connection behind the rear wheels street side, and finally a photo of the toilet relocated between the frame rails.
So it all worked out and is now validated with three 1000 mile travels. Hope this helps.