I haven't tried the Classified 160AW, but I do use the Pro Messenger 180AW. If you're looking for a messenger bag, you might try it. According to the LowePro site, it's just a bit bigger than the Classified. (10.6" x 6.3" x 12" vs. 8.9" x 6.3" x 11.2"). I was pretty much in the same boat, I wanted the smallest, most discrete bag I could find that would hold a 70-200 2.8 mounted on a large body, along with room for a few extras.
I can tell you for sure that it will fit what you have listed, although it would be heavy and the 5Dc body would have to ride in the front pocket.
Right now I have mine loaded with a 1D MkIV w/L-bracket and 70-200 2.8L mounted, 24-105 f4, 100 2.8 macro, 580EX, CP-E4, OC-E3, ST-E2, extra battery, cards, and a few odds and ends. It's packed pretty full, but it's not too bad to carry around slung cross-shoulder. Even this full it's still easy to grab and shoot. Normally I only carry the 580EX and not the extra flash equipment which gives me room to take my 1.4x and 2x TC's and my 12mm and 25mm ET's stacked.
I have a lot of other bags for storing and transporting equipment, but the 180AW and Specialist 85AW are my favorites to work out of. I do also have several different sized Sliplock pouches that attach to the sides when I really pack heavy.
When I purchased the 180AW I did also consider the TT Retrospective 20. It was the only other bag that I found with similar proportions. It seemed like it might be just a tad smaller, so I went with the Lowepro. I might still pick one up for my MkIIN setup. They both had their pros and cons when compared side-by-side, but overall I liked the one I got just a little better. I don't think you could go wrong either way.
Just my 2c worth...hope it helps,