I finally installed the rebuilt speaker and gave it a try. It sounds quite good. I certainly can't tell the different between it and the 37-60 speaker I had been testing with.
I blocked up the radio cabinet bottom temporarily and it does make a noticeable difference for the better. I think I'll cut a piece of masonite to size and mount it with some glue blocks.
I guess that's it for now. Perhaps I'll refinish the cabinet someday
