I've always been amazed by your left-field use of serial ports, not least to generate a video output, of course. I've also heard of people using them as primitive PWM outputs as well, for motor drive projects.
File I/O using the raw cassette data input and output streams has been tackled before, especially, once again, by Martin Lukasec, as in here...
http://www.8bity.cz/2018/tape-emulat...cambridge-mk14
...where he uses an Arduino to 'record' the raw cassette data stream from the MK14 and replay to it. All of his MK14 stuff is worth reading through (there is a 'translate' button upper right on the page, or your browser may offer to translate it).
Your suggested method has the theoretical advantage of needing hardly anything (other than a level shifter) between the PC and the MK14.
Why not have a go?