Thanks to Jazzgirl, Malone & Torquinian.
I'm mightily relieved I'm not the only one who can't parse 31D.
Meanwhile further wrestling has reduced the problems to 3 :
36A - Element of the unknown, letters added to American concerns (4)
B???
42A - Composition of a number's backed with cheers (6)
?O?A?? (Pres SONATA but can't see why) &
37D - The spirit of economy when it comes to map purchasing (10)
????T?E?S?