There are several measurements that are important. On rimmed cases, headspace is controlled by the rim (IE .357 magnum and such). All you need is to manage the OAL in a revolver so that the tip of the bullet does not come out of the cylinder, leading to jams. For a rifle in most calibers, the round is positioned by the case shoulder. IE that is part of the reloading operation, to re-form the case shoulder so that the round will seat fully.
If you can't easily close the bolt, then there are several possible problems. I once had a .270 that was deeply over-reamed. To the point the round would not fire because the round set so deeply in the chamber that the firing pin could not make contact, not that I really would have wanted it to as at the very least, the case was going to be damaged. If the chamber is reamed short, or the case is too long, either would cause your problem. Otherwise, and from your photo this appears to be the case, the round is too long (specifically from the end of the shoulder to the ogive of the bullet) or once again the forcing cone was reamed too shallowly, either of which will prevent the round from seating all the way. You really should be able to chamber a round, lock the bolt, then eject the round and not have any marks on the bullet.
I have run into issues with a .270 when trying to load some pretty heavy bullets. IE say a 180 grain, which since the diameter is fixed, the only way to get that much bullet weight is to stretch the bullet out longer.
My personal fix when reloading was to take an empty (but resized) case and seat a bullet with a light crimp, but seating it a bit shallow so that the OAL is a bit over the spec. Slide the round into the chamber by hand, and carefully use the bolt to seat it. Gently. And with very little crimp, the bullet will be forced back so that the bullet just touches the lands in the forcing cone.
Now, you can take this length, reduce it by the recommended amount of distance (IE for hunting, most use something like .015" or so). If you change bullet types, you have to re-do this measurement to get it right. If you want to go for max accuracy, you can have the bullet BARELY contact the lands, but no more as you risk pulling the bullet out if you choose to unload the gun, leaving gunpowder everywhere.
You seem to have already confirmed that some of the ammo types work just fine. Are the good and bad rounds using the same bullet weight and style? That's one of several things that could cause this issue. A little more taper on the front of the bullet might let it go deeper in the chamber without contacting anything, where a fatter/blunter (or even heavier overall) bullet might touch.
For my hunting rifles, I always depended on two things. First was to try as many types of factory rounds as I could get my hands on. Without fail, some shot much more accurately than others. Second, since I now have a bunch of used brass after this testing, I went through the usual reloading process, knowing that I now have cases that have been fire-formed to my chamber. Resize, check OAL of the case and trim if necessary, then back to the range with various options to try. Several good powders depending on the round, several different levels of powder charge, where ˝ to 1 grain can greatly hurt or improve accuracy. Then there are lots of bullet types and weights. I always preferred ballistic tips, but for no real reason other than the fact that they worked and also didn't collect crap in the hollow point.
That's a lot of explanation for what is likely a trivial issue. All rounds are not created equal. All chambers for a specific cartridge SHOULD be the same, but that doesn't always happen.
AND, to be complete, ammo assembly lines are not perfect. If something goes wrong, say a sizing die slips a small bit, they could produce a bunch of rounds that are too long. So I would not assume it is the gun, I would assume that "something" is off.
For sure, you should not have to force the bolt to close. That is a dead giveaway that something is amiss.
Once upon a time, my cousin and I decided to hunt with single shot rifles to make it imperative that we took good shots since we would not get a second shot if we missed or slightly injured the target. We bought two "handi-rifles" from same manufacturer, same caliber (.270) etc. His liked silver tip ammo and would hit MOA easily. In my gun those were 3MOA rounds, mine liked some flavor of Hornady ammo that I have now forgotten. Same guns. Same models. Same everything. So all things are not really created equal.
Now, back to your regularly scheduled programming.