I am a gigantic moron.
I just realized the 350D's white balance has been shifted to G5 and B4 since I owned it. Sorry for wasting everyone's time
I reset the 350D to 0,0 white balance, and now that they're truly operating at the same level, the 40D is the clear winner - colors are more vibrant, ISO noise is lower, and the colors are more accurate. If I shifted the 40D to G5, B4, I'm sure I could get the "accurate" green color of that blanket just like the 350D was at G5,B4.
Again - sorry