I need to ship a 12" CRT monitor and am wondering if the best method would be to pack it with the CRT face down rather than sitting normally?
Plan to surround the monitor with about 2" of polyethylene foam which is stiffer than bubble wrap but not as stiff as styrofoam and should give good support.
Packing solid styrofoam on the CRT side wouldn't hurt IMO. Put soft packing all around it as you've stated. Also double-boxing is also a good idea. You should be good with that.
I don't remember seeing CRT monitors or TVs packed screen down from the factory back in the day, and I would assume that is for a reason. However, they generally always had form fitting styrofoam and ample room inside the box for it. Doing your best to duplicate that is what I'd recommend. Things like packing peanuts are often no bueno because they shift around and the item packed will end up settling and moving around too much.