Thank you for all the suggestions. I ended up soldering smallest wires I could find and using sharpest bit on the soldering iron, and then I put some hot glue on them to keep them from falling off. It was extremely hard to solder them, this picture isn't doing justice, in real life there's barely any room to work with, but I got it!
I finally dumped the 16MB ROM off the flash chip, I used piratebus 3.6 with very old firmware (as I didn't have my beagleboard nor raspi prepared for SPI reading).
flashrom -p buspirate_spi:dev=/dev/ttyUSB0 -r t430s_stock.bin
It took piratebus 50 minutes. It seems like flashrom can control piratebus on its own, it's pretty cool, all I had to worry about is wiring. Now at the very moment I'm dumping the flash chip again and will compare the hashes.