Does Anyone Know ...

It could be the Living Oracles edited by Alexander Campbell; the 1835 4th edition does not seem to use "thee", "ye", etc. For example --

You are the salt of the earth. If the salt become insipid, how shall its saltness be restored? It is thenceforth fit only to be cast out, and trod under foot.
You are the light of the world. A city situate on a mountain must be conspicuous. (Matthew 5:13-14, Living Oracles)​

Sometimes called 'the first modern version', it was first published in 1826 (that initital edition does have "thee", "thou", etc.) as the Sacred Writings of the Apostles & Evangelists of Jesus Christ which was a compilation of previous work done by 18th century Scottish scholars George Campbell (1789 The Four Gospels, Translated from the Greek the first privately accomplished translation of the Gospels printed in America), James Macknight (The New Translation of the Apostolical Epistles), and English non-conformist Philip Doddridge (1807 The Family Expositor, A Paraphrase and Version of the New Testament) with editing by Campbell against the Griesbach critical text. Shortly after its appearance there was opposition from those that desired KJV supremacy to reign, dispelling the notion that the primary heat of our current translational debate was generated in 1881 with issuing of the RV's New Testament. Some Baptists didn't like the removal of the familiar transliteration "baptism", for example --

But he seeing many Pharisees and Sadducees coming to him to receive immersion, said to them, Offspring of vipers, who has prompted you to flee from the impending vengeance? (Matthew 3:7, Living Oracles)​

I don't own it, but it has been reprinted recently and can be obtained on Amazon for about $20. I do have copies of Moffatt's (both works) and Beck's which I can check; and Lamsa's I'm pretty sure doesn't use "thee", "thou", etc.

 

Alexander Campbell's pronoun plan:
"Excepting in addresses to the Deity, or in the personification of inanimate things we aimed at the expulsion of thou, and substitution of you."

So:
"Our Father, who art in heaven, thy name be hallowed" [1828, 1835]
"And thou Bethlehem" [1828, 1835]

But:
"If you be God's Son, throw yourself down" [1828]
"If thou be God's Son, throw thyself down" [1835]

http://www.bible-researcher.com/campbell-text.html

 

Ferrar Fenton?

"Mr Ferrar Fenton has already published a translation of the New Testament into "current English," . . . . We must protest, too, against [his] use of "you" for "Thou" in addressing the Deity. The plural pronoun not only jars upon one's nerves, but frequently obscures the reference." ---The Critical Review of Theological & Philosophical Literature, 1899.