The bouncing is because you aren't relaxing your leg muscles completely. The more completely you relax, the more fun, faster and safer downhills become. And you get to benefit all the rest of the time too; both riding fixed and on gears since your muscles aren't fighting other muscles that aren't completely relaxed. (The two great techniques for practicing that relaxation are fix gear downhills and riding rollers. Both are not fun at all until you teach your legs that skill.)

A comment re: chain length - any good fix gear chain can be riveted repeatedly with no issues at all. Just make sure you have good (and equal) pin extension beyond the plates. I stay away from the "sexier" chains with shorter pins. (The one KMS 1/8" chain I bough had considerably less pin extension than the Izumi chains I usually use. Yes it ran quieter, but I am much more interested in the chain simply working!)

Ben