I believe that a good crown "Does" make a difference. If you have a 1 MOA rifle, it probably would not make that much difference. But if you have a rifle that is sub 1/10th MOA it could/will make a difference. The problem proving it is that if anyone has a sub 1/10th MOA rifle, they would surely not saw the barrel off to find out.
The last thing that the bullet sees is the crown, and all though the effects may be small, a poor crown can only hurt accuracy.
I have seen benchrest shooters re crown many times to get the best group. I always thought that some of the reason was to tune the barrel harmonics.
The other thing is not knowing if a poor crown has hurt your accuracy or not, so why not put a good crown on it and be done.
If a poor crown doesn't hurt the accuracy, why does every weapon have one, and why are they always recessed ? The recess it there to protect the actual crown (The part the bullet sees is In My Opinion the most important part), the rest of the crown that protects it can be many different shapes.
I'll say this......I have salvaged two barrels, and recrowned them by hand. One was a Rem. 600 243, with a bad rust spot in the last 1" of the barrel that wouldn't shoot. I cut 1.25" off and filed square. Crowned with a round ball, and polished. It will shoot 3/4" groups now, plenty good for a youth deer rifle it was intended for. The next was a 270 WSM Tikka with a buldged barrel. This time I used a hand turn muzzle crowning tool, and it shot several 5/8" groups with factory ammo before giving it back to my buddy. I did both these as a learning experience and achevied what I needed, and in both cases, the only other option was sinking money in to something I really didn't want to do. Would I do it to my Kreiger barrel.....ehhhh, probably not as I expect much more out of that barrel. I think if you're looking for extreme accuracy, try it like JE said, but also as ShtrRdy said if you have 2k rounds on it it may be a crap shot.
Small capacity cartridges like the 6mmBR can outlast 2,000 rounds fired. A 300 RUM will not.
How do you clean the barrel and how often?
Aggressive cleaning with stainless brushes can and will ruin a crown necessitating a freshening of that crown.
Can you document the loss of accuracy attributable to the crown?
Was the loss from one minute to the next, or have you seen a slight degradation over a period of time? Examine the crown under magnification to see if there is degradation or a small ding which might contribute to inaccuracy.
Have you chased the lands or adjusted your load for a lengthening of the throat?
There are lots of questions to be asked and answered before you just whack off an inch of your barrel for a new crown. If the throat is burned out for a couple of inches, it might be time for a new barrel. If the throat has advanced a little bit, maybe a set back is in order or you need to adjust your seating depth. A new crown is a simple solution and relatively inexpensive by comparison but if you need other work done without doing the crown, why bother?
IMO, there is only one way to crown.. That is in a lathe, from the inside out with a sharp postiive h/s tool bit.. Check with a Q-Tip.. Lots of different shapes and profiles will yield good results.. At 2,000 rounds the throat may be eroded.. And if you don't have a bore scope to check there's a great possibility the barrel is carbon and copper fouled..