Tuning Air force Texan 35 cal changing point of impact question

Gentlemen;
I have been shooting my Texan 35 cal for a year now. Came to the conclusion that no matter how careful I am casting bullets, I will never get really good accuracy with them. SOOO, I started shooting Neilson swaged 142 bullets and can get some really impressive groups Then I move those groups to the bulls eye of the target and it's great, BUT when I come to the range the next day, (shooting at 75 yards), the point of impact has changed. Great grouping at that new location, but not over the bulls eye. By the way, I am shooting tethered, 2800 PSI. Velocities within 10 FPS. I readjust the scope and shoots out the center of the target. Come back the next day and the POI has changed again. When you think about it, if you are taking this rifle hunting, the most important shot is that first one. And if you can't trust it to be centered, it really doesn't matter what kind of group you can get. I have a quality scope, have checked everything to be tight, have polished the barrel, and shooting suppressed and as I mentioned, tethered, so velocities are the same. I watch the You Tubes and notice that the guys that are bragging about the accuracy of their gun is good, never move the point of impact to the center of the target. And I notice that when they move from say 50 to 100 yards the groups remain really tight, but they have relocated on the target. What gives????