Why don't you do it the other way around? Get rid of Free, give it the final update, which simply extends the application to just a message explaining your situation, and buttons with a link to the paid version so that they can install it.
And just upgrade Paid to be free.
Thus, your payment customers have the advantage, at least, not to do anything for this, while your free users probably will not want to do the download in order to get more features for which they usually have to would pay.
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