Okay, I've figured it out. It is as described by both the instructions and SD, though I will endeavor to provide a bit more detail for those interested in installing their own.
Note this is applicable to either CookMate or Origo single- or double-burner portable alcohol stoves, as they use the same sort of gimbal brackets.
Each bracket is formed by three plates; there are two brackets for the stove. Part (d) in the above image involves two of the plates. The one on the left in the image is the bottom plate and mounts to your bulkhead (I'll call it the mounting plate). The one on the right in the image is the upper rotating arm of the plate (I'll call it the arm). The third plate is the other big thingy in the image (I'll call it the stove plate) and attaches to the stove. The arm attaches to the stove plate via the thumbscrews, and it is indeed around the axis through the thumbscrews that the stove swings.
The arm is permanently attached to the mounting plate via a sliding hinge. When the stove is not in use, or when it is in use but you don't want it to swing, the arm should be in the "bent" position. If you mount the mounting plate with its bottom edge flush against the bottom of the well in which your stove will sit, then with the stove resting on the bottom of the well, the arm will be bent 90 degrees. Then when you want the stove to swing, you lift it up through an arc until the arm is parallel to the mounting plate, and lower it into place so that the arm "locks". I chose to mount the mounting plate higher up in the well; there's a certain maximum height after which the stove will never rest on the bottom of the well, which I considered undesirable.
All in all, now that the installation is complete, I'm quite happy with the results. The stove is securely mounted, swings through a large arc without meeting obstruction, and can be opened while in the "at rest" position so the "wicks" can be removed and filled.
I've also used the stove a few times -- not while underway yet -- and it brings a can of sauce to a boil in under three minutes. The other concern I've read about the nonpressurized alcohol stoves is in regards to the recommendation that water can be used to extinguish alcohol flames -- it's often mentioned that the use of water is just as likely to spread invisibly burning alcohol around and into the bilge. This would be valid if we were dealing with a basin of alcohol, but in the case of the stove, the alcohol is soaked into an absorbent textile material packed into a wide, flat can. If I needed to, I could douse the stove with water and no alcohol would get anywhere. I've even turned the can completely upside-down without alcohol spilling out, though it was not totally full.
As such I'd recommend the stove to others... easy to use and easy to install once you wrap your head around the gimbal brackets.
Here's the stove in the "down" or non-gimbaling position. The swinging arm is at a smaller-than-90 degree angle because I mounted the mounting plate higher:
And one of it in the "up" position that allows it to swing. Sorry for the mess:
For those of you with the galley-forward model Catalina 27: I mounted the brackets in the vertical line with the mounting point for the swinging cradle that carried the old Kenyon pressurized alcohol stove, good riddance. This enabled the cover to open fully, left some storage space outboard, and doesn't create any interference when the stove swings. I mounted it with bolts through the bulkheads fore and aft of the stove.