Bob,
There is a small piece of aluminum that resembles an "I" beam attached to the swingarm.
The caliper slides on it and then the axle slides through the other end of the caliper mounting . (see cam 22 post above)
I think you may have mis-understood the term "Full Floating".
I by no means am an expert, so please don't take this the wrong way.
This is kind of important as you may lose your ability to use the rear brake... or worse.
If I understand your situation correctly, go out and look at your rear brake caliper. One end mounts to the axle itself. Now grab the caliper and rock it towards the rear of the bike.
(like you were backing up)
look at the inside of the swingarm, where the other end of the caliper was resting,
there should be a that piece of "channel"
That keeps your caliper from spinning all the way around when you apply the brakes.
The caliper body actually has slots that slide on that "beam" and keep it from rotating.
This is why it rotates rearward and pulls on your brake line when you back off the truck...
and when you apply your brakes, the pads apply pressure to the rotor and rock forward hitting the actual mounting point of the caliper....I think...
I'll come back and delete this post if I'm all wet...
Tuck\o/