Using MYSx firmwares should work only to flash Lite-On SHM-165P6S to Sony DW-G120A which is likely why you got the error when you tried it on the SHW-160P6S, You need the PYS2 or PYS3 firmware found via instructions and link in my post #4 to flash your Lite-On SHW-160P6S to Sony DW-Q120A.
You might then be able to flash the resulting Sony DW-Q120A with MYSx firmware if you want cross flash to Sony DW-G120A. Alternatively you could flash current SHW-160P6S to SHM-165P6S using MSOP or MSOR firmware first and then flash with MYSx firmware if Sony DW-G120 is drive desired. It simply depends on whether you want drive to be your original DW-Q120A or the DW-G120A.
Edit: In addition to MYL2 you’ll find MYS3, MYS4, MYS5, MYS6, MYR3 and MYR4 if you follow post #4 instruction except substitute “DW-G120A” in the search box to find Sony DW-G120A firmwares. However, these won’t work on LiteOn SHW-160P6S and will work only on LiteOn SHM-165P6S as explained above in this post.