I never looked for a "deficit" other than as the calories I was consuming either made a change in my appearance, in the tape measure around my waist, or on the scale, consistently each week.
If no change occurs, then I make a small change in my diet and/or cardio.
Your "deficit" is a guess, a starting point. Results are what matter each week and will tell you if you actually are in a deficit, or at maintenance, or in a surplus.
1000 is ambitious, to say the least, but counterproductive if you are looking for the best body composition that you can possibly have when finished. Follow a bodybuilding type diet. Keep protein absurdly high. You don't say what your weight is, but literally there is no amount of protein that is too high. When I was competing, I would hit 300-350 daily. I would say if you are a 6'2" man and concerned because "2lbs a week is still under 1% of my weight a week" then you should be hitting 250 grams daily as an absolute minimum.
Wait, let's do some math. So if 2 pounds a week is less than 1%, then your bodyweight is well above 200 pounds. So look at maybe 300 grams a day. If you can't get there at first, then work your way up. Maybe start at 250 and steadily work on increasing the amount of chicken breast each day. You'll get there.
Keep fats as low as possible. Shoot for 30 grams or so. Never let it get over 50 grams a day even if you eat salmon or something.
Fill in the rest with carbohydrates. Play with the carbohydrates to get the performance you need in the gym and the rate of weight loss desired. You can also cycle them.
Also, play with cardio. You can add cardio in addition to or instead of pulling carbs.