It might be worth it to look into 3.5" drive enclosures. I've got an aluminium one which is a little oversized for a 3.5" drive and which has just the right size for a NUC board and some 2.5" drives (30mm height in total).
It even has a status LED (that's the cable you see) and a kind of sled onto which I can mount stuff.
This might be something you can actually order for $15, but really I meant to give general advice and not a specific product.
It should be
- aluminium so it transfers heat outside
- preferably have this kind of sled so you can screw the NUC board onto it and still get it out of the case
To mount the NUC, tap threaded holes into the base of the sled (or unthreaded ones and special screws which cut their own thread), get spacers (may cut your own from aluminium tube) to put under the NUC and just screw it on from above.
You will also need to cut away material for the ports, with a file or a rotational tool (if you already have one and like using it).
If this is too much manufacturing work for this site, imagine I wrote "Use double sided thermally conducting tape and rip away any parts you don't need with brute force.".
Problem is those things don't have exact spec sheets, so you might need to improvise based on what you end up buying.
