Yes, I am serious about double rifles being able to stand up to as much pressure as a bolt action. (Assuming the rifle is designed to work at such pressures which some are.)

First, aside from the matter of fastening them to the action, there is no inherent difference between the barrel on a bolt action and on a double. For the action itself, it's not a matter of pressure but of back thrust.

The few doubles I have seen after catestrophic blow ups all failed in the outside wall (away from the rib) of the barrel in the area from about the sholder of the cartridge to maybe eight inches in front of the cartrdige. The action remained undamaged in all cases.

The back thrust before corrections is equal to the pressure times the inside base area of the cartridge. How ever there are corrections to be made. The primary one being due to the case sticking to the chamber walls. For a shot gun with modern plastic hulls this correction is small. For a rifle however it's fairly large. This is the reason the inside of the test chamber is lightly oiled in the British method of measuring cartridge pressures.

A 12 gauge 3-1/2 inch cartridge will generate a maximum back thrust of about 6000 lb. A 375 H&H will generate a maximum uncorrected backthrust of around 7800 lb. This is for a SAAMI max load which unlike most SAAMI specs is a bit on the hot side. A realistic load for a double is likley to be less. Now throw in the correction for the case "stiction" and you will probably have less back thrust than the 12 gauge.

Now go look at a cheap 12 gauge double. One that got handed down from grandpa and is probably still tight. Compare it to you DR action. The latter will be built like a brick outhouse compared to the shotgun.

This is not to say you can safely run twice the normal pressure in your 400-450. That rifle was designed to work at normal 400-450 pressures.

A modern 375 H&H double must be able to stand up to the SAAMI max load. The SAAMI spec calls for a maximum average pressure of 62000 lb, 2000 lb more than a 30-06.