Gotcha. I'm a bit flexible on what I'd be willing to do to fit components in a case, and if OP is too then the Node 202 is a good choice.
Here's a couple ways it can be done. Note the second pic, which stacks two 3.5 HDDs, would also allow for an ITX-sized graphics card to still fit as well.
If OP isn't comfortable with alternative mounting methods though then I'd suggest an HTPC case instead since he's not looking to install a graphics card anyway.