Your calculations are pretty close to mine. A 225-40 has an overall diameter of 25.1"(depending on tire brand) An 18" wheel is actually 19" lip to lip.

25-19=6÷2= 3" sidewall. If I leave 1" between wheel lip to fender opening, that leaves me with 19+1+3= 23". Then subtract your 1/2" for flex under weight = 22.5"

The 1 5/8 measurement was INSIDE the wheel opening, from the top of the tire to the bottom of the inner fender. Look at this picture. This was a 50 series tire though. A 225-50 is close to 27" tall. A 225-40 would gain me an extra 1" of suspension travel before hitting the inner fender.