Both 1K and 22K are actually suggested in PBP manual.
So I tried both, I tried 100 ohm resistor, I tried direct connection. No practical difference - actual "junk" bytes are getting different, but proper one still not delivered. The above slow code, suggested by AI, works with either 100 ohm, 1K or 22K.

Currently I'm sending data from 1936 to K80 because K80 has LCD screen so I can use it for debugging. In the real life, K80 will be sending data to 1936.

As a side "improvement", I can use additional data line from K80 to 1836, so SHIFTOUT/SHIFTIN should work then. I guess it will be more reliable?