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That's truly incredible ! Thanks for the edit suggestion, BTW. Realized that ZF + "Can assume ACC but not AC" was really what I had in mind - so was getting puzzled by the downvotes.
Bof: My question is the other way around. I am replacing AC by ACC. So, not clear to me if you can even construct a model of ZF + ACC where CH holds. Also, not sure if forcing requires full AC.
