Even really high-end porcelain bath fixtures can vary dramatically from one unit to the next, it’s just the nature of porcelain. The parts are matched up at the factory after the firing process has shrunk and distorted them. I’ve heard a couple master plumbers tell me that the professional supply houses get the factory firsts, home centers get the factory seconds, and the factory thirds find their way onto the internet. There is no such thing as parts interchangeability in this case, you never really stood a chance of getting a tank lid that fit. Put some gel dots in the places where the gaps are to keep it from rocking and call it good.
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