thank you for thisI think you can do what the OP wants, with a bit of lateral thinking.
The serial data out of the PC serial port always starts with a start (LO) bit, then has the 8 data bits, then a stop (HI, which we can just ignore).
Assuming the baudrate is known, you need an external device to generate clock pulses, as the serial port is already generating the data. This turns the asynch serial into SPI type clk+data two wire serial that can go directly into shift registers.
The external device would detect the start bit, then after a delay of approx 1.5 baud makes a clock pulse, followed by 7 other clock pulses with 1 baud between each. This task could be done with a PIC etc or could even be done using discrete logic chips if you are a masochist.
But the premise is sound; that the PC sends standard serial data and a clock stream is added on another wire, and the two signals can be sent directly into a long chain of shift registers as the OP requested.