[LisaS]

[note: opinion follows]

You have the theory correct, but you must remember that EVERYTHING is a guess and approximation and not a scientific measurement.
METS is an informed estimate of what a theoretical person might burn, activity counters are a guess at METS, GWF is a guess at METS.
Food tables are based on samples of foodstuffs which may or may not match your actual foodstuffs which you may weigh with a greater or lesser degree of accuracy. Water fluctuation, food in your system, etc. can confound even body weight measurements.

So, yes, in theory if you continually adjusted activity and intake to have a constant deficit over a 6 month period, you would have a trend line matching what you expect.

In practice, you'd probably get a similar trend line over a long enough period. If you aren't seeing a trend that approximates what you expect, one or more of your variables could be off and you need to adjust. Perhaps you need a deficit on paper of 825/day (based on your activity calcs and your food measuring) in order to get a trend line that shows 1 pound per week. Yes, the math says 500/day but if you need a deficit of 825 on paper to see it, then that's what you have to work with based on what you can measure & the calculations you do.

Pretty much guaranteed that if you are on a water only fast for a month, you will lose weight and you will greatly reduce your daily activity and you will still be losing at the end of a month. Everything else is a science experiment with n=1.