Since a bleach will remove latent image centers, I would reexpose after bleaching, not before. Also, there may be silver halide grains that are not developable even after reexposure, and these need to go away ---> fixer after second developer.
If you go directly from second developer to fixer, you carry over some developer present. That one minute wash suggested in the Darkroom Cookbook seems a tad short. Fixed out silver may react with developer and form dichroic fog. An acidic fixer will avoid this, but if you use a stop bath and/or a proper wash after the second developer step, you should be able to use any fixer.