If someone is interested in going the DIY route, these are pretty awesome prices for a motherboard you can just buy without having to hunt around for overpriced used stuff on ebay:
B75 ITX motherboard + i3 3240 + 8GB DDR3 for $25
https://www.aliexpress.us/item/3256804955777543.html
H81 ITX motherboard + i5 4590 + 16GB DDR3 for $53
https://www.aliexpress.us/item/3256806808137487.html
There are tons of other options too.
https://www.aliexpress.us/w/wholesale-itx-mot … ctlist.search.0
If you already have an old 3rd or 4th Gen CPU and some DDR3 laying around you can get just an ITX motherboard for under $30.
Like this B85 board for $20...
https://www.aliexpress.us/item/3256807223047663.html
It even has an NVMe slot if you need such a thing. Honestly this is kind of incredible for the price. Has anyone here ever used one of these JINGSHA boards?
EDIT: Throw the board in one of these cases and you can use the included PCI-E riser to have a full height (but obviously still small) GPU in an ITX case:
https://www.aliexpress.us/item/3256806467243079.html
These cases are a thicker than something like an HP T730, but are smaller in height and depth.
Fitting cooling and a GPU would obviously be the biggest challenge. I'm not sure what is possible in that regard yet without doing more research. An i5 4590T or 3570T would probably be a great CPU for something like this though. GPU-wise, the 170MM limit on the length is going to be hard to overcome in a single-slot card, and it sadly rules out the K2200 (affordable, fast, slim, abundant).
If there are any similar options for boards that have a PCI-E and a standard PCI slot, that could be a really awesome all-around solution, though if you can use a full height PCI-E sound card (with a second riser) then that opens up lots of options for newer X-Fi models that still do EAX under XP. You could probably use an NVMe to PCI-E x1 adapter to connect a sound card on one of the boards mentioned above.
More than likely, there are cases that are a bit larger which alleviate a lot of these struggles while still being smaller than the average low-profile SFF system. This is close, but still the max GPU length is just ~10mm too short for a fast single-slot card like the K2200.
EDIT2: If you don't want to mess with an NVMe to PCI-E adapter, there are boards slightly longer than Mini-ITX that have two PCI-E slots... https://www.aliexpress.us/item/3256806378290098.html
I imagine that if you look around a bit on Aliexpress you'll find a case designed to fit these boards too.
There are also super low profile coolers that cost practically nothing...
https://www.aliexpress.us/item/3256806789312257.html
https://www.aliexpress.us/item/3256805765437592.html