Well I'm not sure. George III's marriage policy was quite baffling in that one didn't exist; however the problem here is Frederica was basically the highest ranked bride the Hanoverians could ask for, being the eldest daughter of the King of Prussia. Now the Meckenburg angle is interesting to me as I've never heard of Charlotte disliking her nieces all that much, Frederica being the exception.
@JonasResende, any source on that one? Plus the niece issue wasn't that big a deal, as Adolf Friedrich IV was unmarried and childless, so Karl was his obvious successor. I'd actually considered Louise of Orange-Nassau as a bride for the Prince of Wales but she should work just as well for York, the Dutch being a traditional marriage partner. As for her childlessness, her husband was very much disabled so that was likely the cause.
Now Caroline of Brunswick could be an obvious choice for York, but from what I remember Augusta and George III weren't that close and the King might not want a Brunswicker for his favorite son. What about Louise of Denmark, Caroline Mathilde's daughter? There were rumors about her illegitimacy but I think the British court highly dismissed such claims.