How to add a laptop keyboard to IBM SK-8840 external keyboard?

I have a SK-8840 IBM external keyboard which some of its switches corrupted. The internal board is like the image:

The keyboard connector is a 30 pin, 1 mm. I read this page that Frank Adam made a board to use various laptop keyboards as USB external one. As he wrote there, the keyboard schematic matrix is as bellow:

I connected two different laptop keyboards (Dell, Vostro and Lenovo, Z500) with 30 pin to SK-8840 for testing. As expected, some keys worked but not exactly that keys printed. For example when I pressed ‘z’, ‘p’ has been typed on the computer. So, if the correct pin numbers be connected to the SK-8840, it should work.

Questions: for keyboards with 30 pin or lower pin numbers, how can I determine the column and row pins using only this SK-8840 board? And, how to do a reverse engineering to decode SK-8840? (Note that Adam Frank introduced scanner PCB boards using Teensy which can determine keyboard pins as well as manual method with an multimeter. I think the reverse work would be done by my board.)

Thanks.