The Logistics manager is way overkill for your current gear. I'd have to agree with RLP, the Airport Security V2 is much more appropriate. I have one, and a 300 f2.8, don't forget the 70-200 will stand up in it so takes very little space.
I have taken the Security V2 on many planes and always as carry on, I use it as my everyday bag and wheel it everywhere, if fact I need to send off for a free replacement set of wheels because I have worn them out, the emergency shoulder straps have been a day saver a couple of times too. The Logistic Manager is huge, it costs a fortune and if you filled it up it would weigh so much you'd never move it willingly, if I wanted that kind of case I'd be looking at a Pelican or transport style case.
Here is a shot of the V2 with a 300 f2.8 and a 70-200 2.8IS in it. There is a lot of room left!
Thanks for sharing privatebydesign,
Looking at your photo, It looks I can fit 300mm at bottom and still have enough space for the combo of 5D III + 24-70 II & 5D III + 70-200 f2.8 IS II plus primes.
The two bodies fit across the top, even gripped bodies or 1 series. The sides take four lenses each with hoods, like the 24-70 f2.8, that is single layered, multi-layered I can fit my 50 f1.4, 15 f2.8 and 15 and 25mm tubes stacked in one lens spot, or the 100 L Macro and the 50 f1.4, 600 sized speedlights fit vertically in their pouches along the sides (which is why I don't have many dividers in there). When it is jammed full of gear it weighs well over 60 lbs.
Because if the design of the bag, the telescoping handle part, the only place you can stand a 70-200 f2.8 vertically is in the bottom section, but with all the dividers you get you can put pretty much anything anywhere else.