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What is the best, most accurate way to calculate my TDEE (total daily energy expenditure)?
It doesn't exist and the idea of dropping 500 calories to lose one pound per week (500 x 7 = 3,500 calories in a pound of fat) wouldn't work as precisely as the analytical mind wants it to. See, if you had a “true” measure of your total daily expenditure, you'd find there is no true average - it will go all over the place depending on your stress levels, intensity of training, amount of rest, etc.
In addition, the 500 calories isn't cut and dry. What if you are eating more healthy fats? Or fewer? What if you cut the calories from protein versus carbohydrates? The thermic effect would change the actual amount.
The best way is to be as consistent as possible, then be flexible enough to make adjustments when you aren't seeing the progress you desire.
Let me rephrase that. I can't say that's the best way - I can only say it's the common way everyone I've worked with or know who has been successful has achieved that success.