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How much bump is safe?

To determine if your shoulder bump is enough do this. Remove the firing pin and the ejector. Insert a sized case in the chamber and close the bolt. Increase the shoulder bump until the bolt closes with no resistance.
 
In my opinion, .005" is too close to the lands because variations in ogive and measurement methods can sent you into the lands when you think you are not there.

Assuming you are measuring "bump" correctly, a .002" bump should be sufficient to provide trouble free chambering from a sizing standpoint. You can try a .003 bump, but I suspect that won't solve the problem because it lies somewhere else.

The fact that factory ammo chambers tightly, tells me that something is going on with the rifle. Either a rough chamber, a headspace issue, or an extractor issue that resists accepting the rim of the case. This needs to be evaluated by a professional, i.e., rifle smith.
Yep, .002 for the shoulder bump. I think most of us have stopped chasing the lands and are backing off, oh, .025 in my case. Go on YouTube and watch the Hornady Podcasts, especially
Towards the end the discussion centers around bullet seating off the lands.
 
My bolt closure is tight, even with factory Fed GMM 168.
I sized and trimmed new Hornady brass and set the seating depth at -.005" off the lands. It's also tight.
Next I bumped the shoulder .002" and it's only slightly better, so I think I found the issue.
Question is how much bump is acceptable? .004 or .006?
Did you remove firing pin assembly to check bolt fit? You should be able to safely shoot with up to .008" headspace. It puts quite a bit of stress on the brass however. Unusual that factory ammo would be that tight. Is this a custom chamber? You could have a smaller head diameter on your chamber that's causing the tight bolt closure.
 
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Yep, .002 for the shoulder bump. I think most of us have stopped chasing the lands and are backing off, oh, .025 in my case. Go on YouTube and watch the Hornady Podcasts, especially
Towards the end the discussion centers around bullet seating off the lands.
Several years ago, Sierra use to publish a newsletter. In one of them they discussed seating depth. In their testing they discovered that some rifles do better with the bullet seated .020" to. -030" off the lands.

If you shoot older Rem 700's you had no choice because of the long free bore. In my experience, the 700's I had all shot very well with bullets seated well off the lands.
 
Did you remove firing pin assembly to check bolt fit? You should be able to safely shoot with up to .008" headspace. It puts quite a bit of stress on the brass however. Unusual that factory ammo would be that tight. Is this a custom chamber? You could have a smaller head diameter on your chamber that's causing the tight bolt closure.
It is unusual for sure but in 2021 I purchased a new Rem 700 5R 24 inch barrel in .308. I also purchased new Lapua brass for it. After running an expander in the case mouths to even up the dents and deburring and chamfering as well a case would not chamber without scraping brass off of the head of the case. I fired a few rounds only to find the bolt was locking up and I had to beat the bolt open with the heal of my hand every round. Called Rem and they said if I only shoot Rem factory loads I would not have an issue. I told them I had been hand loading since the mid 90's and informed them of what they could do which was not polite by no means. Sent the barreled action to (WSMNUT) for a re-barrel and never looked back.
 

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