I have completed my work on the list. Here are the results.
Name
Registry
Captain
Assignment
U.S.S. Enterprise
NCC-1701-D
Jean-Luc Picard
Docked at Starbase 173
U.S.S. Yamato
NCC-24383
Richard McKenzie
On Patrol, Sector 134, Neutral Zone
Notes: This is the fourth registry for a ship of this name in this season. The other registries are NCC-1305-E, NCC-71807, and NCC-71808. Richard McKenzie was a set designer.
U.S.S. Constantinople
NCC-43622
Richard James
Special Assignment, Terraform Command
Notes: Terraform Command was mentioned in TNG: "Home Soil". Richard James was a production designer.
U.S.S. Wellington
NCC-33821
Thomas Pucer
On Patrol, Sector 130, Neutral Zone
U.S.S. Farouk El-Baz
NCC-31823
Cari L. Thomas
On Patrol, Sector 130, Neutral Zone
Notes: Cari L. Thomas was a visual effects artist.
U.S.S. Hokule’a
NCC-30187
Robert Metoyer
Planetary Exploration, Sector 130
Notes: Robert Metoyer was an assistant director.
U.S.S. Atlantis
NCC-3210
Dick Brownfield
Diplomatic Mission to Alderaan
Notes: A ship of this name appeared in TNG: "Conspiracy". with a higher registry. Dick Brownfield was a visual effects artist.
U.S.S. []vicker
NCC-31810
Adele Simmons
Planetary Exploration, Sector 142
Notes: This is the first of three ships whose names I am unable to read completely. The first four letters are illegible. Adele Simmons was an assistant director.
U.S.S. []cal
NCC-31054
Elaina Vescio
Deep Space Exploration, Sector 010
Notes: I am not sure how many letters are missing from this name. Elaine Vescio was in charge of set security. Sector 10 was mentioned for the first time in TNG: "Conspiracy".
U.S.S. Neil Armstrong
NCC-31806
Gere LaDue
Planetary Exploration, Sector 142
Notes: This ship might be the same that visited DS9 during the Klingon-Federation war for repairs. Gere LaDue was an assistant director.
U.S.S. Saratoga
NCC-31640
Martin Jedlicka
Deep Space Exploration, Sector 002
Notes: Martin Jedlicka was an assistant director.
U.S.S. Da-Teplan
NCC-30087
Richard Cronn
Planetary Exploration, Sector 054
Notes: Richard Cronn was the chief lighting technician.
U.S.S. Endeavour
NCC-25330
Cosmo Genovese
Deep Space Exploration, Sector 007
Notes: Cosmo Genovese was a script supervisor.
U.S.S. Yorktown
NCC-20045
Gregory Benson
Deep Space Exploration, Sector 032
Notes: This might be the same Yorktown that visited DS9 in 2370.
U.S.S. Excelsior
NCC-21445
Muriel Epstein
Deep Space Exploration, Sector 034
Notes: Muriel Epstein was a special effects technician.
U.S.S. Amber
NCC-21335
Marian Fife
Diplomatic Mission to Alderaan
Notes: Marian Fife was a studio teacher.
U.S.S. Lexington
NCC-30405
Wil Thoms
Planetary Exploration, Sector 028
Notes: Wil Thomas was a special effects artist.
U.S.S. Excalibur
NCC-21534
Al Smutko
On Patrol, Sector 130, Neutral Zone
Notes: Al Smutko was a construction coordinator.
U.S.S. Yuri Gagarin
NCC-25306
Alan Bernard
On Patrol, Sector 142, Neutral Zone
Notes: Alan Bernard was a sound mixer.
U.S.S. []
NCC-30352
Peter Lauritson
Under Repair, Starbase 74
Notes: I was unable to read any of this ship's letters, other than U.S.S. The word is the same length as Apollo. Peter Lauritson was an associate producer at the time of this episode.
U.S.S. Apollo
NCC-30000
Dennis McCarthy
Deep Space Exploration, Sector 002
Notes: Dennis McCarthy was a music composer.
U.S.S. Endeavour
NCC-25330
Cosmo Genovese
Deep Space Exploration, Sector 007
U.S.S. Yorktown
NCC-20045
Gregory Benson
Deep Space Exploration, Sector 032
U.S.S. Excelsior
NCC-21445
Muriel Epstein
Deep Space Exploration, Sector 034
I am not guaranteeing that these results are 100% accurate.