I use the big case all the time (just last night in fact) and have not had trouble. I think you can only have 8 items on it - one item in each slot. Maybe you can stack multiple ingots, but I don't think so. I think your trouble is that each of the 8 slots *has* to be filled.
Getting items on the back shelf can be fussy. The best way I have found is to always fill the lower shelf first, then the shelf helps force things back. It still can be a bit of work sometimes, with gems, to find just the right place your cursor needs to go to get things on there.
Also, if you happen to have "move objects" on, turn it off - you'll never get things placed that way as they "sink" to the floor.
Another thing to try is tilt your view angle so you are looking STRAIGHT down at the back shelf (get it centered right in the middle of your screen) and this often makes it a lot easier to place things. This is also the only way I have been able to place things on the slidable wall shelf from Generations.
Another tip is to get something placed on the front of the shelf and while you are still holding it with you mouse, hit your "m" key which will toggle the item through all the slots on an object. You can use that on any surface - it's quite useful.
Edit: I just caught that you are not on a PC which means you probably have to maneuver differently than I suggest. But the bottom line is, it may be the 8-item/slot issue that is tripping you up, which would be true no matter what form of the game you are playing.
