Patience paid off. I got a floating brake off ebay! Just sitting down and compressing the rear suspension shows how it could help. Before installing it with the brake held the bike would move forwards and backwards as you bounced on the seat.
With the floating brake it still shifts forwards and backwards, but not nearly as much.
The downside of it is I think it will make the bike rattle a bit because of how it's made.
I'll take pictures of it later if folk want to see it. I'm thinking somebody here will also want me to put it on a piece of graph paper, then measure the hight, bearing bores, etc.. right?
Oh, a question for all of you who have these. What's the difference in the 3 settings the floating brake can be screwed into?