Can't seem to make double-buffered painting with multiple monitors

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These highlighted must just match in their top left

They do match. If you check above the left-top of RECT is set to 0,0.

As for setting mapmode, I'm not really sure what you mean. Can you give a code example of what should I add? It might be it, because I don't think there's anything else I can do with this sample. It seems right.