I wonder if it may be time to DIY a transfer program on the Lisa side. It is at least possible to
send 8-bit data from a program running on Lisa OS over the serial port; the YMODEM implementation I made requires it, so the problem does not lie in the Lisa OS serial driver or in the OS libraries. But setting YMODEM aside, I've mooted a wire "protocol" for text file transmission upthread, which Alex's python program could reproduce with minor modification; the major work of course is on the Lisa side.
I barely have time to tie my shoes these days (after-market elastic drawstring shoelaces for the win), but if I were doing this I would start from
LIBPORT.TEXT and write a function called TimedReadLine that reads "\r"-terminated lines from the serial port (the few string library functions starting from PDF page 142
here may help).
From there on it's a matter of reading lines and then writing them to files, I should think.
The largest source file (APDM-DESK.TEXT.unix.txt) is under 256k, so we might even consider loading all incoming files directly into RAM, provided it's not difficult for Workshop programs to allocate so much memory. Storing file data in RAM should be about as fast as it gets, and that would maximise throughput. But this would be something to fix only after a simpler approach was working, I think.