Okay.. I finally found a datasheet that illustrates the issue: http://www.mouser.com/ds/2/222/KMDAX-xS-20587.pdf
There are eight basic pin locations for mini-DIN sockets, and you just leave out the pins you don't need for a given connector. The center key is the problem: it is indeed in different locations for the 5-pin and 6-pin variants.
From a design perspective that makes sense.. you use keys to prevent misalignment and just-plain-wrong connections. The side-lugs and shroud (that stairstep thing on the end of the male connector) prevent misalignment, but the key keeps people from plugging a lower-pin-count male connector into a higher-pin-count female connector. Usually that kind of thing is Bad.
In your case, there are a couple of options:
First - you can make the keyhole on the 6-pin connector larger. From your photo, it looks like the key in your connector is sloped on the side closest to center, so a little grinding with a Dremel or X-Acto knife will give you the clearance you need. Frankly, you could probably drill out the whole center without causing any trouble.. just leave some plastic between the edge of the hole and the pin sockets.
Second - you could get a female mini-DIN-5 connector. Here's a link to a list of options: http://www.mouser.com/Connectors/Circul ... ricing%7C0
That would cost you a few more dollars and add some delay though.
Third - you could cut the key out of your keyboard connector. I include that more for completeness than as an actual suggestion, because while I have no problem hacking up hardware, I get all sentimental about *vintage* hardware. My old Apple ][ is more of a pet than a project opportunity.
It does look like linking to a 6-pin adapter without checking for compatability was an oversight on the Adafruit crew's part though. I'll flag this post and let them know there's an issue.
When you void a product warranty, you give up your right to sue the manufacturer if something goes wrong and accept full responsibility for whatever happens next. And then you truly own the product.