Thanks
@BeeMaa
The rimmed, low pressure cartridges are better choices for a double rifle than belted magnums. I state this owning a Blazer S2 in 375 H&H and a Heym in 458 Win.
Neither rifle has any problems with the spring loaded pawls that ensure extraction and/ or ejection.
Headspace issues? Who told you that?

Maybe they referred to any break action gun or rifle, after thousands of rounds, the action may loosen and need to be put back on face. The higher pressure belted cartridges will in theory cause this type action to loosen faster than lower pressure rimmed cartridges. In theory, but overall these rifles on average don't fire 1,000 rounds in a lifetime. In face, not many centerfire hunting rifles do!
The above paragraph concerns a double rifle loosening up after shooting many rounds. A Heym in a high pressure chambering should last much longer without loosening up than an entry level double. Be careful what bargins you buy!
My Blaser is very accurate and is a space age marvel of engineering design!
My 40-year old .458 Heym regulates Cutting Edge Raptors and Safari Solids well enough for 100 yards kills on plains game. Note, I mounted a Trijicon SRO with a 1 MOA red dot which affords better accuracy for me or anyone requiring reading glasses. Long ago Jack O'Connor advised that when a man needs reading glasses, its time for him to switch from metallic sights to a scope.
Both rifles mentioned were offered to me a great prices. If I were buying new, I would select either a 450/400 or a 500/416 for a medium bore double. If fact, I think the 500/416 is a great chambering for a hunter/client double. A PH should however have a .45 bore or larger to save my bacon, if necessary!
All the above stated from mostly my experiance and a little opinion, if however someone offers you a well regulated .375 H&H at a great price, buy it! But and here's the twist, well regulated for a .375 is not the same as for a .470 or .500 NE. These large bore double rifles are mostly a single purpose weapon. They provide stopping power (even if not "stopping rifles") for large critters at close range that can and will kill you. While I like better regulation, two shots from each barrel in a 3" circle at 50 yards or meters is good regulation for .45 bore and larger.
Medium bore double rifles especially those chambered for .375 H&H should be much, much better than 3" at 50 meters! My aforementioned Blaser S2 shoots more like 4 shots in a 2" circle at 100 yards. I previously owned a Merkel in .375 with a scope that would shoot similar groups at 100 yards. Those rifles to me could hit accurately on targets or plains game to 200+ yards.
Buying a double is an experiance. How does it regulate what ammunition? If the seller cannot show you targets with factory ammo or handload data, one is taking a risk that the rifle will hit center with both barrels at much over 50 yards. BIg bore, okay fine. Medium bore, I want more accuracy at somewhat longer ranges.
Bottom line is that a medium bore, belted magnum double may be an excellant choice if it is well made like a Heym, Blaser, or in most cases a Merkel. My Merkel later developed trigger problems... Pawls to extract a cartridge function fine but may in time fail. Those double pawls on my .458 Heym still function perfectly after 40 years. Finally, yes higher pressure cartridges will put more stress on any action, bolt or break, than will lower pressure cartridges. That stated, I'd stay away from any entry level double in a high pressure cartridge.
The above is worth exactly what you paid for it.