Just downloaded and about to listen.....with some trepidation ;D
I hope very much that you managed to get something out of it; that trumpeting seagull coasting over Brooklyn Bridge has always struck me as being at least as naturalistically evocative as any passage in Delius.
The only "problem" insofar as it might be said to be one) with this work, its same composer's Double Concerto for Piano, Harpsichord and Two Chamber Orchestras and his Triple Duo and much more recent Double Trio - not to mention the "double duo" that is his impenetrable (to me!) Third String Quartet - is that most listeners, especially if listening to a recording or broadcast, will be no more aware of the specific subdivisions of forces (let alone their significance in the scheme of things) than would be the case with the peripatetic soloists in such very different works as Thea Musgrave's Clarinet Concerto and Colin Matthews's Horn Concerto; it's what I suppose I might call the "Gruppen / Carré factor", to the extent that these things can only really be fully appreciated in the context of live performances and, even then, are accordingly more visual than aural issues. That, however, in no wise undermines Carter's A Symphony of Three Orchestras as a work.