On the C&C side, I currently have the Players Handbook, Monsters & Treasures, Monsters and Treasures of Airdhe, Of Gods an Monsters and will also fit any of the three versions of the CK screens.
If you don't like my mix, you can create your own by swapping out books. You can fit your CKG, but you'd have to remove 2 books to get it to fit properly, or one thicker supplement (Not thin like the Players Handbook but more like the Monsters and Treasures of Airdhe) and it will stick up between 1/8 or 1/4 depending on the book removed. So if you don't care if it sticks up a little then the CKG will fit sans one book. If you put two books that are about the same thickness as the Monsters and Treasures of Airdhe, there wouldn't be enough room for the screens. But, again, if you don't mind the lid of the box sticking up slightly then this isn't a problem.
There is enough room, on the upper/lower ( Depending where you want to put your dice
) inside, to put dice in, but they'd have to be placed side-by-side or stacked, depending on how many dice you want, without a dice bag. Unless your willing to take the time to use a dice bag and place the dice as need be, or some other way. (Felt to separate the dice from the books?) I'd be hesitant to just place the dice without some kind of barrier between the books and dice as I don't know what the dice would do to the books as you carry the box around.Edit: I just fit 2 sets of dice, stacked, (Both do not have 3d6 just 1d6) in the box using my Crown Royal dice bag. (Happy to say the same Crown Royal bag from the mid 1980's. Still the best dice bag of all time.) Using the bag, it was easy to line them up on top of the books and move them into the place. It also makes it pretty easy to stack the dice so you can fit more dice. (I can fit 3 sets of dice, but it takes more effort. So it is possible to either add another set of dice or add those 4d6 that are missing.) An unexpected bonus is adding the Crown Royal dice bag it fills the space so now any books you have in there do not shift around, making the whole package very stable. I might also add that I have the landscape screens. The top of the Crown Royal dice bag folds nicely into the space that the screens don't cover. This leaves me to believe that it wouldn't work with the other two CK screens. Though if you have small individual dice bags you could fit all 3 in the space, then there would be room for any of the screens as there is nothing you need to fold to get it to fit. There is also no "bowing" of the box if done properly. It stays true to form.
As cool as the Erol Otus picture is the Pete Mullen version is still nice, but is darker than what is shown on the BHP webpage. I guess it could be interpreted as showing a dark evil dungeon atmosphere, but I hope that subsequent printings lighten up the tone a bit.
All in all, if you were on the fence about these boxes I hope my little review pushes you to the side of, "wanting to get."
