If you have a working firmware dump that you want to flash then getting a CH341a + SOIC clip to directly write the flash chip might be the most obvious solution.
If you have access to u-boots serial console (but sounds like you don't?) then you could interrupt u-boot and transfer the firmware into ram using e.g. the ymodem protocol, and then use u-boot to flash write that onto the chip. I don't know much about these switches but early on in this thread it read like the default u-boot requires the password Hs2021cfgmg.
Edit: regarding the .bix file, the binwalk utility suggests it has a 64 byte header after which LZMA compressed data begins. I don't know if the switch expects this format for firmware updates or not but when flashing I'd strip the first 64 bytes off.