These are always hard to tackle without in-hand inspection. This is a difficult one as it has symptoms indicative of possibly more than one issue. Pressure related, ammo related or gun related.
One thing I do with belted mags is use a small base die or a collet die to resize the body just in front of the belt. If that area expands enough after a firing and many times a conventional sizing die won't re-size that area enough... sticky chambering/extraction can result. Since the 375 HH has quite a bit of body taper, it's usually not a big issue. But I have gotten into the habit of never saying never :) Just a possibility that popped into my head as I was thinking about this.
You said it seemed "mechanical". Something easy to inspect- close the bolt on empty chamber of course. Set safety to "mid" position (90' from bolt). Lift bolt and remove. Study the small tear drop shaped detent on the shroud opposite the safety lever. It should be popped out about 1/8" or so. It is called the "bolt sleeve lock". If you rotate the sleeve (shroud) you'll notice that if the bolt sleeve lock is depressed the shroud (sleeve) will rotate and the sleeve lock will pop into a slot on the boss of the bolt handle. If released, the bolt sleeve lock will lock the sleeve in that position to the bolt body. Slowly put the bolt back into the receiver and keep an eye on the detent action of the bolt sleeve lock as it contacts the rear receiver ring. Then rotate the bolt as per a normal cycle and watch the sleeve lock and sleeve (shroud) in relation to the bolt body.
I think everyone has given good advice about headspace, pressure and brass, so obviously those issues should be looked at first. Then maybe do an easy inspection of the bolt sleeve lock. If it doesn't depress properly and doesn't slip freely into the slot in the boss of the handle (part of the bolt body) it could have a slight "catch" during regular bolt cycle and operation. Won't hurt to look at it and won't take any time. The next mechanical thing to check may be the safety itself as it interacts directly with a boss on the striker. These parts can wear or even chip and cause issues. But probably best to do one thing at a time :) If it is a mechanical problem and not a brass or pressure issue, at some point, if not corrected or identified, it may require a visit to a competent Win 70 gunsmith- but hopefully not! Good luck on finding and correcting the issue.
1st pic shows pen pointing at bolt sleeve lock on sleeve (shroud) and the slot it fits into when depressed by the rear receiver ring on this post 64 Win 70 bolt.