I don't ship anime cels that often- but I do sell 
the EVA repro cels and the Kenshin Nishikie and 
what I do is I cut up 2 of the smaller boxes- 
(one I trim 1 side so it will fit, and slit 
the side of the 2nd one- hard to explain)cut off 
the flaps for both, stick the cel/nishikie in 
between that, (so there are 4 layers) tape it up, 
stick that in one of the large Priorty mail tyvek 
envelopes and then stick it in a flat larger 
envelope.  Then I rip off the backing and seal the 
package. Then I slap on my "DO NOT BEND" labels.  
I figure that's pretty safe since it between 3 
layers of cardboard on either side and the tyvek 
is waterproof and free!  It seems like more work- 
but if you cut prepare a bunch of them (trimming 
and slitting, and getting rid of the flaps) while 
watching t.v or something.

I shipped about 40  packages that way and have 
never heard about any damage.