The Children of Húrin, Beren and Luthien, The Fall of Gondolin.

The last Houghton Mifflin Harcourt deluxe edition was The Fall of Arthur in 2009.  Though Harper Collins is headquartered in New York, and owned by News Corp, also headquartered in NY, and has been actively marketing to you, the USA collector since 2008... by strict definition there is no US deluxe edition of Beren and Luthien or The Fall of Gondolin.  The Easton Press fine bindings are superior, but they are only printed every several years, and sometimes only sold in sets when available.
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The Children of Húrin
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First Edition  2007
Dust Jacket, Fold-out Map, Illustrated by Alan Lee
Small hardcover, black paper over boards, 8 color plates, 25 black and white sketches.  The first printing was sold out at HMCo before the release date;  the fourth had been ordered within a month of it.  RRP $26.00
ISBN:  0618894640   ISBN-13  9780618894642
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Book of the Month Club Edition  2007
Dust Jacket, Fold-out Map, Illustrated by Alan Lee
Small hardcover, black paper over boards, 8 color plates, 25 black and white sketches.  Except that this edition has no price printed on the jacket it is practically identical to the trade edition.  Out of print, RRP $14.99
ISBN:  0618894640   ISBN-13  9780618894642
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Deluxe Edition  2007
Paper over boards, reinforced spine, slipcase with gilt decoration and cover pastedown.  Illustrated by Alan Lee with 8 color plates, 25 black and white sketches.  Not quite up to previous standards of "Deluxe", but at least it makes the trade edition look weak and sad.  RRP $75.00
ISBN:  0618904417   ISBN-13  9780618904419
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Easton Press Leatherbound Edition  2007
Ribbed spine, AEG in 22k gold, moire endpapers, ribbon placeholder, bells, and whistles.  Illustrated by Alan Lee.  Sometimes available through www.eastonpress.com.  Original RRP $90.00
Publisher Product Code:  1840
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First Paperback Edition  2008
Trade softcover, fully illustrated by Alan Lee.  RRP $7.99
ISBN:  0547086059   ISBN-13  9780547086057
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Del Rey, First Mass Market Paperback Edition  2010
Cover illustration by Alan Lee.  Available new, RRP $14.95
ISBN:  0345518845   ISBN-13  9780345518842
Beren and Luthien
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Houghton Mifflin Harcourt First Edition  May 4, 2017
Hardcover in Dust Jacket
Illustrated by Alan Lee.  RRP $28.00
ISBN:  1328791823   ISBN-13  9781328791825
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William Morrow Paperbacks, first US trade edition, March 6, 2018
Trade Paperback
Illustrated by Alan Lee.  RRP $28.00
ISBN:  1328915336   ISBN-13  9781328915337
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Easton Press Leatherbound Edition 
Ribbed spine, AEG in 22k gold, moire endpapers, ribbon placeholder, bells, and whistles.  Illustrated by Alan Lee.  Sometimes available through www.eastonpress.com,  RRP $111
Publisher Product Code:  3329
The Fall of Gondolin
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Houghton Mifflin Harcourt First Edition  August 30, 2018
Hardcover in Dust Jacket
Illustrated by Alan Lee.  RRP $30.00
ISBN:  1328613046   ISBN-13  9781328613042
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Easton Press Leatherbound Edition  2018
Fine Binding
Ribbed spine, AEG in 22k gold, moire endpapers, ribbon placeholder, bells, and whistles.  Illustrated by Alan Lee. 
Publisher Product Code:  3456
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Wheeler Publishing   April 24, 2019
Large Print Library Binding Edition
Glossy pictoral paper over boards, illustrated by Alan Lee.  RRP $37.99
ISBN:  1432863266   ISBN-13  9781432863265
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Houghton Mifflin Harcourt   September 3, 2019
Trade Paperback
Illustrated by Alan Lee.  RRP $16.99
ISBN:  0358131456   ISBN-13  9780358131458