200 mm IS: a hole in Canon lens line?

I've had the following lens lineup for my Canon 35mm and DSLR
cameras (all canon lenses):

24mm, 28-135 IS, 100-400 L IS, 500 f/4 L IS, + 1.4 and 2x TCs.

I always found the 100-400 soft. I could make fine 8x10 enlargements,
but not critically sharp larger ones. So, I replaced the 100-400
with a 300 f/4 L IS (very sharp). But now I have a hole from
between 135 and 300 mm. What I want is a 200 mm f/2.8 L IS lens,
which at present does not exist in the Canon lineup).
I've heard the 70-200 f/2.8 L is sharp, but what do you think?
How about the 200 f/2.8 non-IS?

Roger