I love this and have experienced this exact thing. I have found that the combination of food journaling plus activity tracking works very well. I have described it as “budgeting” just as you did.
Psychologically I have found that it increases the immediacy of rewards for good short term decisions — if I choose good portions of low calorie foods earlier in the day, by evening I might get to treat myself to something special in the evening and still run a deficit. Without that kind of motivation a series of good micro-decisions only has long-term benefits which are a harder sell when you’ve got a craving for something.
I used both he FitBit Surge and the Apple Watch for activity tracking. I chose to do food entry through MyFitnessPal which can use FitBit activity data to adjust your allowed calories for the day. It works very well, I dropped 25 pounds and 5 inches from my waist while very rarely feeling deprived. I wrote about it here on Medium too.