finally i read this book - Пушки для боевых самолетов, А.Э. Нудельман, 1993 - well, it's just about guns in total, have some interesting details, but no more than "n-37 was tested on yak-9 and serial production started later" ie no any news for us, but, have technical information about ns-37 in total and report about lagg-3...
well, report confirms number of shells,
36, what very logically - 120-140 shells for shvak and 30-32 shells for ns-37, for yak-9, in compare 150-160/36 for lagg-3 - and have information about rate of fire, max. 290 after some shots, min. 232 after some shot, average 258 what confirms technical description of ns-37...
personally i think what info enough and it's can be fix already now, especially, because 20 vs 36 it's really difference...