Finally dug out that old board and soldered two 1k resistors. PS/2 to Amiga adapter now works without problems.
I planned to do something like integrated PS/2 adapter and mouse switcher that I gave up on when this didn't work. Now I can redo it again
. Only thing to ponder about is if I only put pull ups on fire buttons or on every pin. And probably it's only needed on pins coming from PS/2 adapter side. Joysticks are simple pull to GND.