If you're doing regular file transfers, I suggest looking to Kermit. For moving files around, short of needing to do whole disks, I've been using kermit server running on an Ubuntu box and kermit on the kaypros with one of these wi-fi modems:
https://www.cbmstuff.com/index.php?route=product/product&product_id=113. 19,200 file transfers work well with this setup though any kind of interactive terminal doesn't at that speed, I guess because of the slow screen updates (and I think the device is helping buffer the 19,200 a bit plus adding in network buffering). But this setup should work well serial-to-serial though I never managed better than 9600 kaypro to kaypro with serial.
There is a pre-built Kermit for Kaypro, and even some instructions for building a minimal loader to pull Kermit over, though I didn't try those.
Also check the baud rate you are expecting, and of course crank it down low at first as you test to get things working. I believe the program on the standard kaypro disks that sets the baudrate is called "baudm" (one called "baudP", I believe, sets the printer serial port). Or if you're using KPLUS Roms or Advent Turbo ROM the baud rate can be set there.
I understand the appeal of the nostalgia if you're just trying to see if you can get the serial transfer to work with bare bones utilities, but on a more practical level, using something like a GoTek, to get files over is more practical especially if you're moving lots of files.
Lastly, the "drive just spinning" sounds like the machine is hung up, so maybe something more basic going wrong here.