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Wikipedia (bless it ) informs us that the Earl of Warwick hoped to continue to rule through Edward and was pressing him to a marital alliance with a major European power. Because Edward secretly married Elizabeth Woodville he alienated Warwick.
So...
Let us keep Elizabeth Woodville as a (more or less) secret royal mistress, and have Edward make a continental marriage. The question is, who would be the bride?
Over to the residents of the forum for suggestions...