In a different thread I estimated 7 people in a standard Azuma carriage, assuming optimal spacing. The chances of being the only person in the carriage are slim I'm afraid
It can be odd sometimes: from the Leeds the 0945 can be busier than the 0845. I'd say that mid-morning (1015 to 1145) or mid-afternoon (1345 to 1515) are your best bets, based on my own experience. Also, don't go with the default reservations if booking through the LNER website, assuming they still allow you to change your seat. From memory they book you into C and G first if a nine-car Azuma, B and A tended to be quieter as people don't wait to board in those carriages. C and D go first in a 225, B and E/F are quieter (but E & F are near the centre).
As ever, this is my experience; other posters' experiences will vary. And good luck.