How can I make a PC look like a thumb drive for reflashing devices?
Many embedded linux boards and possibly some laptops can be configured to do this (as can Android devices)

USB devices that act like external hard drives or flash drives implement the USB Mass storage class 

You need a board or device that has a USB On-The-Go compatible USB port . Here's an example of a suitable linux board that should give you some pointers.

You will need to write the software to select and present your disk images to the system.