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What is it you want to pull from the homepage? Some copy-text of a couple of hundred words?

I would recommend not to pull it off, as it works and seems to work good. What is it you want to gain by removing it from the homepage?

Since Google already found the most relevant page on your site for the kw (combination), I would say that things would not change. I assume that the general site topic remains the same - even though you remove the text from your homepage (about how much text is it? just text? links as well? <- if yes .. this is where it gets tricky).