I just picked up a set of these
SL-A400 7-speed shifters on sale from Nashbar for super cheap. They seem to fit fine on the pods I got from Rivendell. I also recently fitted a different set on the pods for a friend. I used his 6-speed indexed Shimano SL-1050 down tube shifters, produced in 1986, and original on his bike purchased new in early 1987, and those worked too.
BUT, I do believe you're having a legitimate fit problem with yours. As I recall, some of the other Shimano shifters from the mid-80s did have a thicker base cover... And, Shimano seemed to market a billion similar but slightly different models every year during the 1980s.