My 375's barrel is thick enough not to be effected very much at all by a mag tube dovetail. Would be similar to a sling swivel mount on the barrel of an express rifle, the rifle itself is not a target gun.
If you want to improve the accuracy, the most effective way I have found on a Marlin or Win big bore lever gun, is to change the sights to a more effective sight set and do an action job to improve the trigger pull.
Also found that a wide field of view, low power, scope, like a 2x, in a tip off mount, is very effective on the Marlin big bore hunting guns. The Marlin side eject is already set up for a center mounted scope. My tip off mount returns to zero, so can use the iron sights or the scope at will.