I would suggest the Zotac GTX1050 or 1050Ti Mini GPUs. They are the smallest available full height cards.
There are a couple things you should be prepared to do. Those cards have Legacy BIOS. You will need to turn off Secure Boot in BIOS, and maybe turn on Legacy Compatability Mode. Or get an ITX card that has native UEFI support. But figure out which way your card will run.
The other thing is to boot into Safe Mode (F8), create a System Restore point, and remove the GPU drivers for the onboard video.Your newGPU should boot into Safe Mode+ Internet with no drivers installed. Some drivers can only install in normal Windows mode. But the default Safe Mode resolution will still start up.