Upon key on, the cpu verifies the checksum and if INCORRECT, it will rapidly flash the check engine light. If the check engine turns on at key on, then turns off briefly then turns back on solid. That means it passed the checksum verification.
The Willem should be fine as well as many available. We just need a good read. I haven't found any of the tables wrong in your read although I only checked a few, so, you are close :)
It should be a 27c128, some programmers are better if you choose 27128. You will have to see how yours acts, these are very old chips so contacts are sketchy :(
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