OK, I'll explain the cowls.
The first one was the MKI, which has 3 metal tabs around the lip, which the plastic starter cover screws into. These 3 metal tabs rest in 3 square indentations in the lip, and the lip itself is a flat, squared of rim. There are also 3 holes, in these 3 indents, which the screws pass through.
The MKII Cowl, as well as the Early MKIII cowl, were made from the same cast, so while the 3 screw holes are gone, the 3 indentations are still there, and there is a noticeable ridge running around the lip.
The later MKIII cowl, does not have any indentations, nor is there a ridge, the lip simply slopes down at the edge of the hole.
If you get your MKIII cowl, which i know to be a later one, and compare the lip around the starter hole to your MKII cowl, you will see what i mean.
The MKIII base i have here waiting for you is an early MKIII base, and it takes the exact same cowl as your MKII, not your MKIII.