It all sounds eminently sensible but the final bill is many times what I would expect. In a 3 bed semi, with an inefficient boiler, a not dissimilar heating pattern to yours and a unit price of 3.77p, my annual bill is hovering around £500, which many will say is too high. I really can't imagine where your gas is going providing the heating controls are working as you believe. My boiler never comes on at night for example and I've only noticed it once during the day, even during this cold spell.
I guess you need an expert eye cast over the system, to account for your present usage. Sorry I can't help more.
Andy C