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The Pelican 1620 will hole everything except possibly the 7" AB reflectors. If you can use a space for the reflectors nested and cables and cords the setup might work out fine.
This is in part why I like using Quantum Qflash as they work with either reflectors or the collabsible Norman 19" softbox-umbrellas. Takes 10 seconds to pop the Norman open and have softbox or to put on a hood or to use the flash bare bulb. Nice having full TTL, compatibility with Nikon or Canon i-TTL and e-TTL and having RF wireless range up to 600 feet and fast ratio adjustment.
I used standard studio strobes and hauled them around in custom cases before discovering the Quantum which provide more than enough power, have battery packs, lots of available modifiers, road tough, compact, and bullet-proof. I shrank my lighting kit by more than two thirds and have a faster setup, faster adjustments of the lighting, and faster take down.