I have a set of 18" x 11" HRE three piece wheels. The 305/40/18 drag radials (from a different manufacturer) I currently have on them just will not hook. I'm running a 2010 Camaro with a 440 engine and a manual transmission and 3.91 rear gears.
I see that the recommended rim size for the 325/40/18 is 12". Will they work on my 18" x 11" if I keep the tire pressure low?

Yes, an 18 x 11 will work. You can go plus or minus 1 inch with the tires.