The UV erasable one is only in DIP, all other packages have no window and therefore cannot be erased. My quick seach also suggests the SOP44 version is unobtanium, it wasn't common to begin with... but you can try to locate MX29F800 flash or some other 29F800 part. Aliexpress seems to have this part available, then you only need a dump and write the chip.
The basic idea is that flash chips (29Fxxx of some sort) have a pin to control writing to the chip, that ROM and EPROM chips do not have since they are not writable in-system, and it is usually in place of a address line. You have to disconnect that address line and rewire it to where it is supposed to go, and connect the !WE pin of the chip to high state to put it into permanent read mode. Looking at the board photo above, there is an extra address line connected to the pin that is !WE on flash chips, that is actually not used on the ROM itself, perhaps for possible future 2MB ROM model that never materialized... So you have to cut that trace, and connect the pin of the chip to VCC (or leave the trace connected and cut it some location where it goes near VCC and then bridge it there if it can give a more desirable result).
Looking at the pinout of MX29F800, there's also an extra !RESET signal that has to also connect to VCC but it is right next to the !WE pin so a solder blob can connect those together. Stealthy mods are possible with some effort though.