Well, you are trying to control calorie deficit (or surplus) by calculating X (intake) and Y (output) to arrive at Z = X - Y
The first problem is both X >> Z and Y >> Z. Hence a relatively small error in X or Y leads to a large relative error in Z.
Both X and Y have sources of error.
In the case of X, the main issue for me is eating out or eating food prepared by other family members. This might be why I was losing so much weight between Christmas and New Year.
In the case of Y, there is the base energy expenditure figure you use (about 2200kcals in my case) and additional output, such as cycling. The figures I get from LiveStrong are much higher than the values I calculate from the Powertap, for cycling. However, this doesn't mean they are necessarily wrong, because the Powertap measures energy at the wheel, and then I estimated calories by multiplying by 4.2. This is necessarily a lower bound because it doesn't include all sorts of energy such as that used to balance, hold your weight up, move your legs, and drivetrain losses.
The typical value for this is 20kcal/kilometre for me, but hard riding (e.g. Fred Whitton) is 25kcal/km and the ride from Dalkieth to Esdalemuir was around 30kcal/km.
If I put bicycling at 14-15.9mph (vigorous) I get a figure around 30kcal/kilometre which is about 50% higher. It is about 10% less for moderate cycling.
It might also be that the estimates calorie burns are for a different type of bike that you and I ride.
I don't think it's a reason to abandon this approach, but I think you need to monitor the results and if it's not working, then you can make adjustments to compensate. Better that than give up.