In addition to what 44 AMP offered, I will point out the idea that short bullet jump is an essential ingredient to accuracy is something that was assumed to be true because a lot of benchrest competitors either jammed bullets in their rifle throats or swore by one particular short jump or another as a universal truth for accuracy. Subsequently, this has all gone out the window.
The first clue I recall was in the 1995 Precision Shooting Reloading Guide. Benchrest competitor Dan Hacket described a 40X 220 Swift he could not get to shoot 5-shot groups into under 3/8". At the time, he was subscribed to the idea 0.020" of bullet jump was ideal and loaded all his rounds that way. Then one day, while switching bullets, he accidentally turned the micrometer on his seating die the wrong way and loaded 20 rounds 0.050" off the lands. When he fired them in groups of 5, he got two 1/4" groups and two true bugholes in the ones. So much for 0.020" off the lands.
The second clue was an online article describing a program Somchem used to have at their facility in which they would tune loads for a customer. One day they had a fellow show up with an old 8 mm Mauser with a badly worn throat. It looked shot out to the Somchem tech, but the fellow said it had belonged to his grandfather, and he wanted to hunt with it again for sentimental reasons. So the tech worked up a load and started moving the bullet back. Every time he moved it back, the group got smaller. In the end, the rifle wound up shooting the smallest groups ever seen in the development program. Some like 1/3" C-T-C or a little better, IIRC.
The third thing was
this article by Berger that came out before their hybrid bullet ogive came out.
Similar findings for other bullet types and by other folks testing the concept started to show up.
Scott Saterly, a top-ranked nationally known precision rifle competitor, has said he's now loading about an eighth of an inch back from the lands.
The bottom line is that if you load to maximize cartridge concentricity, have a concentric bore and chamber, and get your brass loaded without too much head clearance, you likely have all the aligning you need, freeing you to try different seating depths, as the Berger article suggests. I have a theory about why benchrest competitors held to the short jump for so long, but I don't want to go into it here. Suffice it to say it was overdue for challenging long ago. In your shoes, I would go the Berger route but probably reduce the initial step size to 0.020" if you are not shooting the long VLD nose profiles. Shorter profile, shorter steps. This is because the annular gap between the bullet and throat increases more quickly with seating depth using a stubby ogive vs. a long one. Dr. Lloyd Brownell demonstrated way back in 1965 that this affects pressure by how readily it vents bypass gasses as the case neck opens under pressure.