KatLondon wrote:

But there was a little chink, maybe half a mm, near the opening where the cord had to go through.

 For future reference: the half mm chink was on the spring itself, is that right?

KatLondon wrote:

It was between the spring and the drum. Just in one place. It doesn't show in the photo, I just thought - you know, I could get a screwdriver tip in there...

Good to know.  I will file this information away as someday I may have to replace a similarly attached drawband.  I have been lucky so far - convenient hooks or slotted openings on the mainspring drum for securing the drawband.