I would have thought that 6" is neither here nor there when it comes to shotgun patterns. If the centre of the pattern is 6" below the POI of the rifle at, say, 40 yards you still have a fair bit of the pattern above that POI. I wouldn't have thought you'd have much excuse for not killing a beaver or whatever else.
That said, there are a couple of other things you might try. One is trying different loads, both rifle and shotgun, to see if you can narrow the gap. A somewhat stiffer load from the shotgun, for example, may pattern a bit higher, while a change of bullet with the rifle may alter elevation (and, due to harmonics, this can be difficult to predict).
The other thing you could try is one you already mentioned, and that is regulation. While the Savage doesn't have provision for it you could consider the way other combos like the Baikal achieve it, by way of applying a bit of pressure to the barrels to deflect (bend) them. The Baikals do this with a screw between the barrels at about the midpoint, which screw obviously you don't have, but you might try using some shim stock or similar to achieve the same effect, either at the midpoint (bending the midpoint of the rifle barrel up a fraction) or in the muzzle bracket to apply some force downward on the rifle barrel. Once you've found the sweet spot you just need to fix the shim stock in place and Bob's your uncle.
Personally though, if the shotgun barrel was centring its pattern a mere 6" low at 40 - 50 yards I'd be inclined not to worry about it. I wouldn't have see-through mounts on a bet. I'd have a scope with a low magnification (I find 1.5-6 ideal for combinations), mounted low, and sight in for the rifle barrel. Using the shotgun I'd look right through the scope, focussed on the target and ignoring the reticle, putting any ideas about aiming out of my mind. I've shot lots of running and flying critters precisely that way - even shot a bit of trap that way.
