Hi,
As far as I can see the schematic and the sequence are o.k.
What about heat, does the LM293 become hot? Too hot?
What about the 12V supply. Is it stable? --> DVM
Do you have a scope to see the input an output voltages of the driver IC?
If not you should stop your program at each of the four steps and measure the voltages with a DVM.
If you see no heating you could use half step mode:
0x80, 0xC0, 0x40, 0x60, 0x20, 0x30, 0x10, 0x90 and back.
If you see heating then try with "cooling phases" = 0x00
0x80, 0x00, 0x40, 0x00, 0x20, 0x00, 0x10, 0x00 and back.
Klaus