Ted over at Microcore Labs has been developing a modern Z-80, which he calls MCLZ8, which can plug directly into a Model III.
MCLZ8, is a Zilog Z80 emulator which can be used as a drop-in replacement for the original Z80. It uses a Teensy 4.1 microcontroller board which contains an 800Mhz microcontroller and a small PCB to perform the voltage translation between the motherboard and the microcontroller. The MCLZ8’s Z80 emulation passes the exhaustive ZEXALL opcode test suite and the speedy microcontroller allows the ability to simultaneously mimic the Z80’s local bus interface.
You can read about his project here.
Some videos of the MCLZ8 in action are here.