***
On the Columbia single James/Sinatra CD there are airchecks along with the studio performances. Those airchecks were the same as previously released on Hindsight. Hindsight has no more James/Sinatra material. The original air check transcriptions were returned to the James Estate. The combined 16 tracks released on the Big Band Memories box set and the single CD All Or Nothing At All on Hindsight are of all the songs Frank sang during the live appearances. ***
Hello Peter,
maybe we are talking about different CDs? I had in mind the following:
The Hindsight CD „All Or Nothing At All“ (HCD 263) has the following airchecks featuring Sinatra vocals:
07-13-39 New York City, Roseland Ballroom
I Poured My Heart Into A Song (#11)
07-31-39 Atlantic City, Steel Pier Marine Ballroom
To You (#10)
08-05-39 Atlantic City, Steel Pier Marine Ballroom
From The Bottom Of My Heart (#8)
Let’s Disappear (#16)
08-10-39 New York City, Roseland Ballroom
My Buddy (#2)
Melancholy Mood (#6)
08-31-39 New York City, NY World’s Fair, Flushing Radio Building
All Or Nothing At All (#4)
Here Comes The Night (#13)
11-09-39 Hollywood, Victor Hugo’s
On A Little Street In Singapore (#15)
Where as Columbia/Legacy CD „Harry James & Orchestra“ featuring
FS (CK 66377) has the following airchecks, which are different from the Hindsight CD:
07-08-39 New York City, Roseland Ballroom
Stardust (#15)
Wishing Will Make It So (#16)
07-10-39 New York City, Roseland Ballroom
If I Didn’t Care (#17)
The Lamp Is Low (#18)
07-24-39 Atlantic City, Steel Pier Marine Ballroom
My Love For You (#19)
08-10-39 New York City, Roseland Ballroom
Moon Love (#20)
This Is No Dream (#21)
I don’t have the Big Band Memories Box set, so I assume the Columbia tracks are all on that Hindsight Box (since they are not on the HCD-263)? Do you have the catalogue number at hand? Would love to locate that box somewhere. (Or is it the HBCD-503 3 CD set mentioned in the HCD-263 liner notes?)
Great notes and layout on the Hindsight HCD 263 by the way. A well done CD in my opinion. (Same goes for the Columbia one, too). "Produced and compiled by Pete Kline"

Congrats!
Thanks,
Bernhard.
PS: There is one more track adding to the above 16, "All Or Nothing At All" from 07-19-39 (NYC Flushing), released on MastersOfJazz MJCD 53, but of course the song itself is already featured.