p0420 will not be resolved until a new cat converter is installed and code has been cleared. Good to hear your idle is now roughly in the right area, is any accessory turned on such as A/C or heat? That will cause an engine load to increase RPM.
My car does that too, but at 5th gear on 45 mph area, but mine shakes the roofline, but that's caused by harmonics from the transmission. You have to realize that your car has lots of vibrations and hums that the human ear cannot hear nor feel. Sometimes it can be from gears or mechanical moving parts, like for a good example, a camshaft spinning without pistons compressing is annoying loud, we hear it on a engine dynamometer when breaking in a camshaft for racing applications, but when the engine is completely turned over and running, you wont hear the camshaft anymore.
2009 Cobalt LS XFE U74
Mods: K&N Typhoon Intake, Option Cat-Back Exhaust, Cosmo Short shifter, Maxxim Ahead 17X7's, MPx shorty antenna, FE5 Strut/shocks, Tein S Techs, Moog endlinks, Moog spring seaters, ZZP shorty header, LSJ downpipe, LNF front grille