About the bullet scrape. Could that happen when you push the round out of the magazine and up into the chamber? You might try partially chambering a round from the magazine, extract it and look for the mark. If that shows the issue, that would imply an issue with your magazine, mag catch, or feed lips.
I thought about it and the only other place where you could get that scrape would be if there is crud or a burr where the chamber shoulder meets the neck. Here is the thinking. Once the case shoulder enters the chamber, that scrape would not happen until the bullet enters the chamber neck -- if you put the case shoulder just into the edge of the chamber, the ogive of the bullet might touch the opposite chamber wall but the scraped spot would be protected. As the round is pushed into the chamber, the bullet might touch the lands but that is the wrong mark for lands -- those are dashes or square spots on the ogive. If there was some crud or a burr -- something pretty hard -- where the neck meets the shoulder -- that could make a scrape like that.
One other observation: the scratches in the scrape are straight fore-and-aft. The round was not being twisted when those scratches happened. Another argument that the scrape happened as the round was leaving the magazine.
Regarding difficult chambering: it will take a little force to make that scrape. Your description is not precise enough to guess if the chambering difficulty is caused by forcing that scrape into the bullet. If it is, then you have your answer. If not then you may have a second issue. The classic reason for hard bolt closure is that the cases are too long. Clean a case and try to chamber it. If it is hard to chamber then the brass is too big. We don't know where it is too big -- neck length, neck diameter, shoulder headspace (most likely but not established) or shoulder diameter, body diameter, base diameter or rim diameter -- but it is too big somewhere. Take a magic marker, blacken the entire case (you can also smoke one over a candle or oil lamp but smoke is very tricky to do) and chamber it. Wherever the marker scrapes off is the place where the interference happens. If nothing scrapes off then I suggest that you bump the shoulder. Nothing scraped off because you are just pushing the case straight forward and there is no sliding or rotating action to scrape off the marker. Start long and very carefully work shorter. The key test is to chamber the piece of brass.
The best test happens if you remove the firing pin and the ejector from the bolt. You have it right when the bolt almost, but not quite, closes freely on the case. If the bolt handle just drops freely, that is a little too short. All of the tests for brass and chamber size are best performed with a bare bolt, without a firing pin or ejector.
Once you get your die set, resize a few more pieces of brass, to validate your setting. If you find that the brass is too long, RCBS makes a pretty decent case gauge. I use one to diagnose issues like this.
One other possibility - not impossible but unlikely - you may have a particularly robust ejector spring or there may be some crud in it. The bolt face has an extractor hook that catches the rim and a spring-loaded ejector button that pushes against the opposite side of the case base. When you pull the bolt toward you, the empty brass clears the chamber and ejection port and that ejector flips the case out of the gun. If it was full of crud, it might put higher-than-normal forces against the base and push the brass against the side of the chamber opposite the ejector. When you rack the bolt back and forth, the ejector pushes against the 7:30 position on the case base. When you close the bolt, the ejector rotates to about the 10:30 position. If you pull the barrel to look for issues in the chamber, look in the upper right quadrant - between 12 and 3 for a burr. In my experience, a dirty ejector stops working -- the crud makes it push less hard, apparently the opposite of your issue -- but it seemed worth mentioning.
One other thing, eyeballs are not calibrated but the neck looks long to me. The 7.62/.308 trim to length is 2.005. I cut mine to 2.008+-.001. If yours is over 2.020 things may start to happen. While you have your calipers out, check the rim diameter, the standard is about .473.
