We had 3/4" of rain today. Time to do some indoor work. I marked the opening with a pencil, using a carpenter's square to get it, well, square. I made the opening about 1/16" too small, then filed it using a 1" wide "Mill ***" file. Sorry, that is what it is called. As it turned out, I did not need any method of holding it in place, as it is a snug fit. I did grind off the projections that were molded into the Lionel dome for use with the spring, as they no longer served any purpose, and were in the way.
After finishing it, I realized that you could add a dome to any car, and it does not need to be centered. The "Real" car earlier in this thread was an observation car, sort of like a passenger train caboose, and its dome is offset to the rear.