Yes, that does make sense. The class 66 bobbins are 'taller' in the middle than they are at the edges.
Just for fun, I got out my 319, which is much like the 306, and tried a 66 class bobbin in it. It does fit, but as you experienced the middle part of the bobbin sticks out from the case. The "L" bobbin is indeed flat. There used to be an image here on QB, with a bunch of different bobbins in a row. I can't find it now. I did find
https://www.sewingpartsonline.com/bl...y-sewist-know/ and the bobbin for the 306 is shown as #2. The bobbins that I think you have is at #7
Janey - Neat people never make the exciting discoveries I do.