The blues -- you can intensify the blues a lot by a brief bath in a weak solution of Potassium or Ammonium dichromate. Do this after you have fully washed the print (then re-wash). I put the cyanotype in a tray, pour the dichromate solution over it, then pour the dichromate back in the bottle. If you wash the print well, the dichromate will last a very long time.

Hydrogen peroxide will only hurry-up the natural oxidation that will happen anyway -- and not give added intensity beyond that.

The success with the rod will be paper-dependent -- some papers may have too much sizing to work well with the rod (and have difficulty accepting from the brush, too -- which might be the cause of your "beading up".) With platinum, I use the rod to establish the print area, then finish up with a brush.