Of related interest...

   The American symphony / Neil Butterworth.
   Aldershot (England) ; Brookfield (Vt.): Ashgate, c1998.  338 p.
   Includes bibliographical references, discography, and index.
   ISBN: 1859284590 (hb)

While the book has many omissions and inaccuracies, it also has some works
previously unknown to me.

Looking over the list...some of my choices for "great" American Symphonies
Limited to works I have heard...with the exception of the Harris Second
which I have in score.

Adler: Symphony No.2
Albert: Symphony No.1
Barber: Symphonies 1,2
Becker: Symphony No.3
Bernstein: Symphonies 1,2
Binkerd: No.2
Blackwood: Nos. 1,2
Carter: Symphonia
Copland: all 4 (including Dance Symphony)
Creston: Nos.1,2
Diamond: Nos.1,2,4,6
Finney: Nos.3,4
Foss: No.2 (Symphony of Chorales)
Goeb: Nos.3,4
Gould: Nos.1,3
Gruenberg: No.2
Haieff: Nos.2,3
Hanson: Nos.3,6
Harris: Nos.1 (1933), 2 (have the score),3,5,6,7,9
Hill: No.1
Hovhaness: Nos.1,2,15
Ives: Nos.2,4
Kurka: No.2
Lees: No.3
Lewis: No.4
Luke: Nos.2,4
Mennin: Nos.3,5,7
Persichetti: Nos.4,9
Piston: Nos.1-8
Riegger: Nos.3,4
Rochberg: No.2
Schuman: Nos.3,5,6,7,8,9,10
Sessions: No. 5
Shapero: Classical Sym.
Thompson: Nos.2,3
Vincent: Symphony in D

Butterworth includes several composers that I don't think of as being
American...people like Toch.  His 2nd and 3rd are wonderful works.  And
then there are all of those that I would love to hear...the unrecorded
Goeb, Hill, et al.

Perhaps I less critical but I really do believe all of the above works
are amongst the finest symphonies ever written.

One of the most interesting listings in the book...a Symphony by Stokowski!

Karl