Well, if you want to keep going in the same direction, yes, a DC in, DC out, SSR will do the job. Just make sure that the peak voltage at the output of you AMP is high enough to turn on the SSR, but not too high to "destroy" it !!
As for the rectifier, you can simply use 4 simple diodes hooked up like in your diagram. Once again, make sure that their voltage rating is higher then the peak voltage of your AMP stage.
But once again, as Hero999 said, there are simpler ways to do it.