ATmega8 happens to satisfy those requirements. It's also not too hard to program microcontrollers that would support human level inputs.
In practice, the bootstrap device will be like a Windows7 laptop we've got squirreled away somewhere. It's probably cheaper to buy up a ton of used / old laptops that are sufficient for bootstrapping rather than trying to build methodologies that bootstrap from scratch.
Of course you can also try to reprogram the BIOS ROM on the motherboard, but you're likely to need a full OS to first reverse engineer it enough to know where to stick your debugger code.
For example, you could build yourself a makeshift hex keyboard and load a driver for that keyboard onto an ATmega. Good! from that point on, you can enter bytes faster.
Then, you hook a few seg7 together to have some kind of display. Even better!
... and so on, until you can drive that FDD.