They are to similar in sound for me, as nn they would be fine or with one of them in the middle name slot as you have suggested.
Looking at the other names in your profile I think
Rufus Nye sounds okay.
Not really sure what else to suggest it works well with all sorts of names as long as they dont have an N at the beginning or end of them or a strong an Eye sound
David Nye,
Edward Nye,
Jacob Nye,
Philip Nye,