Gymrat76 is right, go for backpack.
i have a safrotto (equivalent to 400AW) and can only fits in
dslr with attached wide angle (reverse hood) + bat grip, sigma 20-300mm (reverse hood), 50mm 1.8, 28-105mm & 550EX flash.
if i use LowePro Mini Trekker, it can put in the above with additional body(w/o lens), sigma 70-300 and also another 420EX flash.
But the weight will be a problem!!
IMO, get backpack as you forget to include flash in.