Welcome to the TBG Forum, HughC!
So, with those particular dimensions, we have to be pretty careful about the case you use. Specifically, 11" wide would be very narrow for a horizontally-oriented case. Most cases are much wider than they are deep, but you have a bit more depth than width available. And you absolutely won't be able to find anything off the shelf with the specifications you need. The big OEMs just aren't focused on this specialized market. You want slim, compact, Blu-Ray compatible, true 4K output, with an SSD - that's simply non-existent. But of course we can build one, right?!?
Actually, your options are pretty limited, but I think you could actually get by very nicely using a 7th-generation Intel NUC with 4K support and an external Blu-Ray drive. It will be tiny and have everything you want. Here's the parts list:
(1) Intel Nuc 7th-Gen i3: (Amazon.com
(2) Pioneer external Blu-Ray drive: (Amazon.com
(3) 8GB of Crucial RAM: (Amazon.com
(4) Crucial MX300 275GB SSD: Amazon.com
(5) Windows 10: Amazon.com
(6) Cyberlink PowerDVD 16 Blu-Ray software: Amazon.com
Total cost comes to about $675, and going with the NUC that I linked to allows you to add another SSD or hard drive later on if you need one.
If you have a strong desire to have the DVD drive integrated, then we need to custom-build an HTPC, but you'll probably be limited to the IN-WIN BQS656 (Amazon.com
) due to size restrictions. I've reviewed this case and like it a lot, but it adds a lot more bulk and could end up more expensive.