I don’t worry about trying to store the base and everything else as one set. The base is just too bulky (especially in granite) for me to consider that.
For the “Everything else” part of the equation, I stumbled across a kinda neat fake book case at Hobby Lobby one day that works pretty well (I think it cost 15 bucks):
It holds my diamond and ceramic stones well
And my other wicked edge “junk”:
I keep my strops in ziploc bags to keep em clean and the pastes separate:
The whole kit packs up nicely:
And I store it upright on a shelf next to the base in my office: