Found something on eBay that gave me an idea.
For about $150, you can buy old laptop motherboards with pretty good dedicated graphics (i.e. https://www.ebay.co.uk/itm/794987-501-HP-Envy-15-with-Intel-i7-5500U-GeForce-GTX-870M-Motherboard/233592673972). If a cooling solution could be fashioned up, it could be an absolute price-to-performance king with an external monitor and some kind of jerry-rigged case.